Tottenham Hotspur 4 - 0 Everton
Cenk Tosun made his debut but struggled in another abject attacking display from Everton
Everton were completely out-played by Tottenham for the second time this season, going down to a heavy 4-0 defeat.
Cenk Tosun was handed his full debut following his arrival from Besiktas in a £21m move last week but the Turk spent the hour he was on the pitch mostly chasing shadows as the Blues once again failed to register a shot on target.
Instead, it was the prolific Harry Kane who stole the show once more after Son Heung-min had put the home side ahead after 25 minutes. The South Korean converted a simple chance from Serge Aurier and then created a similar chance for Kane to score two minutes into the second half, albeit from a suspiciously offside position, to effectively kill off Everton who were dreadful throughout.
Kane added his second just before the hour mark with the visitors' defence embarrassingly flat-footed while Christian Eriksen finished one of the best moves of the match by sweeping home inside the last 10 minutes.
The talk for Everton coming into the game had been about Tosun and Allardyce's admission that, having improved defensively, he and his team now had to add goals and entertainment to their game. The new signing was reduced to jumping for long balls downfield and vainly running the channels, however, while the defence crumbled at the other end.
Son's flicked header off an Eriksen free kick in the 14th minutes was the first sight of goal for either side but it flashed over Jordan Pickford's crossbar before Rooney was put in by Tosun's flick but he dragged a shot across goal and wide.
The veteran forward had the ball in the net midway through the first period, this time off Tosun's nod-on from Gylfi Sigurdsson's corner, but his goal was chalked off for offside.
The game sparked into life at that point and Pickford had to make a double stop to keep Spurs at bay, parrying away efforts by Kane and Aurier and then diving to his right to stop another shot from the England striker three minutes later.
Tottenham made the breakthrough when a switch ball to the right flank caught Cuco Martina well out of position covering an opponent in the centre and Davinson Sánchez's low centre was tapped in by Son.
Kane doubled the lead following an error by Jonjoe Kenny who committed himself against Son and was left stranded as the Spurs forward surged into the space behind him and delivered a dangerous ball into the six-yard box that was turned home as simply as the first goal.
Pickford saved from Kane again and Son hammered a shot off the post before the home side's goal machine added another when he stole in behind Mason Holgate to bobble Eric Dier's centre over Pickford's despairing gloves.
Allardyce used all three substitutes to almost no effect as the second half progressed and Everton all but disappeared from the contest. Pickford kept the score down two more stops to deny Son and Alli but he was powerless to prevent the fourth from going in with eight minutes to go.
A flowing Tottenham move ended with Eriksen firing home from Dele Alli's flick to complete the rout.
The Toffees remain in ninth place and still sit seven points above the drop zone but have not won in almost a month. The humiliating defeat was Everton's fourth in succession in all competitions and extended their winless run to six games, erasing the initial steps forward taken when Allardyce first arrived.