The Blues led at the break thanks to a beautiful Leighton Baines strike from 18 yards and a typically confident penalty from the same player, but despite their relative comfort David Moyes's side couldn't add to their tally and handed the Baggies an unnecessary lifeline.
Indeed, having had almost nothing to do for over an hour, Tim Howard's first real involvement in proceedings was to pick the ball out of the back of the net with 25 minutes to go and a combination of the visitors' lack of attacking threat and adequate defensive work by Everton's back line for the remainder of the game would leave the American mostly untested throughout.
The same could not be said for Ben Foster in the Albion goal who was relieved to see Kevin Mirallass, a surprise starter after being withdrawn early from Saturday's FA Cup win at Bolton, drag a 25-yard effort wide and then Marouane Fellaini's 20th-minute strike rattle off the outside of the angle of crossbar and post.
The visitors' goalkeeper was powerless, however, to stop the opener when it arrived just before the half-hour mark. Steven Pienaar played a nicely-weighted through-pass into the path of the over-lapping Baines and he smashed a sublime shot inside the near post from just inside the penalty area.
And the England international was handed the opportunity to double both his tally and Everton's lead when Claudio Yakob, recently on as a replacement for the injured Thorne, clumsily hauled Victor Anichebe down in the box leaving referee Michael Oliver with little choice but to point to the spot. Baines did the rest with typical aplomb and the Blues led 2-0 at the interval.
With that platform, Moyes might have expected his charges to press on in the second half and put the game to bed but they emerged from half time a little sluggishly and, not surprisingly given their predicament, West Brom began to have more or the possession and do more of the probing.
It was Everton, though, who continued to carry the greater threat and Pienaar sent Mirallas away down the left channel but Foster beat the Belgian's shot behind after he had turned the closest defender.
Clarke's first change after an hour was an attempt to bolster his side's attacking options as he removed James Morrison in favour of Shane Long and the substitute pounced to capitalise on an awful double error by Heitinga within minutes of being introduced.
The Dutchman completely lost Lukaku, allowing the Belgian striker to steal in behind him but having won the gamble when the striker choked his shot and the ball came to him on the goal-line, Heitinga turned a routine clearance off the line turned into an awkward attempt to half-volley clear and Long nodded the ball home before he could get a boot on it.
Moyes responded by taking off Mirallas, who had looked lively, a little rusty, but surely relieved to have come through an hour's action unscathed, and threw on Gibson to tighten things up in midfield, where all of Pienaar, Phil Neville, Fellaini and Osman were keeping the home fans on edge with sloppy play in possession,
It almost disaster a couple of minutes later, though, when Dorrans smashed a direct free kick off the face of the crossbar as the home started started to rock a little defensively.
Still, Everton pushed forward looking for a killer third goal and penalty claims erupted again from the home fans when Yakob appeared to drag Anichebe down and in the ensuing melee, Osman almost turned a loose ball home but it was a yard too far in front of him.
With the home fans re-finding their voice, Osman then danced his way past a flailing challenge and let fly from 20 yards but his left-foot shot was always rising over the bar. And after Dorrans had fouled Baines on the left edge of the area and set up a free kick opporutnity, Foster had to be alert to palm Pienaar's shot over the bar as it threatened to creep under the bar.
3-1 arrived on a gilt-edged platter soon afterwards after two Pienaar shots were stopped by Foster and then a defender but with the goal yawning in front of him Osman, presumably looking to steer it above any attempted blocks, somehow managed to put the shot over the bar when it was almost inconceivable to miss the target.
Thankfully, it wouldn't matter, and though the slender lead made it a less-than-easy finale, Everton were fairly comfortable while Albion resorted through desperation to launching the ball forward in the closing stages.
So, three vital points that gets the team back to winning ways after two goalless draws in the League, pulls them within one point of Tottenham in fourth and provides a timely boost in morale. Better still, both Gibson and Mirallas made successful returns from injury and while Nikica Jelavic, benched for the first time this season as his goal drought continues, wasn't able to make any impact as a late substitute, things are certainly looking bright at Goodison Park as the Blues prepare for a second successive home game against Aston Villa on Saturday.
Lyndon Lloyd
A midweek Premier League clash at Goodison Park under the lights; progress in the FA Cup; revived optimism and buzz around the stadium with the news of an exciting-looking signing.... Shades of a year ago when Everton's stuttering season really kicked into life following the January arrivals of Steven Pienaar, Nikica Jelavic and Darron Gibson and a barn-storming 1-0 win over Manchester City.
The Blues were 10th with 29 points following that game but they come into this midweek match-up with West Bromwich Albion with 38 points on the board and a superb platform from which to launch a challenge for fourth place over the last 15 games, the like of which Everton haven't had since the 2004-05 season.
Since starting 2013 with a terrific win at Newcastle, the team's form has dipped with two disappointing 0-0 draws against Swansea and Southampton that were under-pinned by iffy performances and a worrying lack of cutting edge up front.
So the impending acquisition of Leroy Fer from FC Twente, the hope of at least one more new face arriving before the transfer window closes on Thursday and the consequent lift in morale could come at just the right time to reignite the Blues' campaign as they prepare for back-to-back home games.
Should all go to plan with Fer's medical it's unlikely he will be registered in time to play any part against the Baggies but he will surely be unveiled to the faithful before the game and his presence alone should excite the fans. The lingering feel-good factor provided by John Heitinga's last-minute at winner on Saturday, meanwhile, will hopefully galvanise the players.
The Blues will certainly need a spring in their step and fire in their bellies for what will be another tricky encounter against a well-drilled side. Steve Clarke's West Brom may have slipped a little from their eyebrow-raising early season form which saw them running neck-and-neck with Everton among the Premier League's top four — they've only won one of their last four — but they remain a stern test, particularly given their strong defence and the physical threat up front posed by Romelu Lukaku.
Prior to the goalless frustration against Swansea two weeks ago, the Baggies were the only team to have stopped David Moyes's side from scoring this season. Their 2-0 win at the Hawthorns on September 1st was one of only three times the Blues have been beaten in the League and the thirst for revenge will hopefully provide an added edge to Everton's players.
With an eye on the visit of Aston Villa just four days later this weekend, Moyes may be tempted to tinker with his team so that fatigue doesn't become a bigger factor for his regular starters but a perennial lack of options may preclude significant changes.
Darron Gibson hinted to supporters in the away end at the Reebok Stadium at the weekend that he will be fit to play after missing the last month with a recurrent thigh problem, but Seamus Coleman is likely to miss a second successive game with a thigh injury of his own and Kevin Mirallas' continuing hamstring issues make him another unlikely participant.
And then there is the increasingly thorny issue of Nikica Jelavic who has scored just one League goal in 14 now and who has been substituted in the Blues' last two outings. Moyes insists the Croatian will come right and may therefore continue with him in attack — particularly if Gibson does return, allowing Marouane Fellaini to play the second forward role — but Victor Anichebe has been pressing hard for inclusion recently as well.
At issue, too, is the right midfield position where Steven Naismith has struggled to make an impact since arriving from Rangers in the summer. Magaye Gueye was deployed in that role at the Reebok on Saturday after Mirallas was forced off and almost marked his return to the first team with a cracking goal but he, too, has looked far from convincing despite being given numerous opportunuties to shine.
One option that Moyes has so far resisted, mostly likely because of the effectiveness of his partnership with Leighton Baines when it is in full flow, is to push Pienaar over to the right flank and play Bryan Oviedo on the left. The left-footed Costa Rican looked suspect when played on the right flank himself a few weeks ago but the South African is a lot more versatile and would adapt more readily to a position in which he has played before.
Whatever starting XI Moyes eventually opts for, it's going to be vitally important that his team starts with and maintains an intensity and desire to win what is the first of a succession of vital games in their quest for Europe. While Chelsea still battle to find consistency, Tottenham remain in reach and Arsenal breathe down the Blues' necks, the race for 3rd, 4th and 5th Premier League places is very much heating up but the margin for error will decrease ever more as the weeks wear on.
If Moyes can find ways of turning draws into victories, starting with two from the next two home games, he will keep his team very much in the hunt with a trip to Old Trafford looming in less than a fortnight's time.
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