Wayne Rooney struck his 200th Premier League goal but it wasn't enough to lift Everton over City at the Etihad
Everton came within 10 minutes of claiming their first win at the Etihad Stadium in seven years but were pegged back by Raheem Sterling's volley in an incident-filled contest.
The Blues had played the previous 40 minutes a goal up following Wayne Rooney's 200th Premier League strike and with a man extra after Kyle Walker was sent off for two bookable offences but couldn't hold out for three priceless points.
They faced almost ceaseless one-way traffic after half time as Manchester City belied their numerical disadvantage with mounting pressure and Pep Giardiola's men eventually found the breakthrough in the 82nd minute before Morgan Schneiderlin also saw red in controversial circumstances late on.
Ronald Koeman had countered Guardiola's three centre-halves with a five-man back line of his own, deploying Mason Holgate as the right wing-back, starting Tom Davies in the centre with Idrissa Gueye and Morgan Schneiderlin and dropping Davy Klaassen to the bench.
Dominic Calvert-Lewin played up top with Rooney and the wisdom of the Dutchman's game plan quickly became apparent as the young striker put in an excellent shift as the target and hold-up man in attack.
The 20-year-old had Everton's first attempt at goal, a speculative effort across Ederson that had the Brazilian scrambling across his line to see it past the far post, and then teed Davies up for a shot of his own but the midfielder dragged it well wide.
At the other end, Nicolas Otamendi drew the first save from Jordan Pickford with a long-range effort that the England U21 keeper pushed away but only as far as Sergio Agüero. He tried to lift the ball over him and into the far corner but Phil Jagielka was on hand to head to safety over his own crossbar.
Agüero was foiled by brilliant covering work again by Jagielka in the 33rd minute but looked to have carved the Blues open a minute later with a precision cross to David Silva at the far post. The Spaniard brought it down expertly but slammed his shot off the woodwork.
A minute after that, Everton took the lead. Holgate advanced into space towards the City penalty area and slipped the ball to Calvert-Lewin who wrong-footed his marker deftly before squaring it to Rooney. The veteran forward sent an accomplished first-time shot in off the ‘keeper to make it 1-0.
Rattled, the home side tried to rally into the interval but when Walker appeared to clatter through Leighton Baines, he picked up his first booking and then collected a second just two minutes later after Calvert-Lewin went down clutching his face following an aerial collision with City's home debutant. Referee Robert Madley went to his pocket again and flashed Walker another yellow card.
Guardiola responded to the setback at the start of the second half by withdrawing Gabriel Jesus and introducing Sterling and the pattern of the second 45 minutes was soon established as City took control but struggled to create clear-cut chances against Everton's resolute back line.
Rooney had a momentary opportunity to slide Calvert-Lewin after terrific distribution by Pickford had put the defence on the back foot but his pass was overhit and he headed a later free kick straight at Ederson. Otherwise, it was virtually all the home side, particularly in the final half hour, even after Gylfi Sigurdsson had come on for his debut.
Bernardo Silva bounced a half-volley wide, Sterling then drove over the bar twice in as many minutes and Pickford saved well from Danilo as he tried to fire a shot underneath him from the angle.
Everton's goal was breached for the first time as the game moved into its final stages, however, and in unfortunate circumstances. The otherwise excellent Mason Holgate could only head a cross from the right back to Sterling in a central position in front of goal and he made no mistake by sending it past Pickford into the bottom corner.
Having been booked as early as the seventh minute, Schneiderlin had been walking a tightrope all evening and when he was adjudged to have fouled Agüero late on, referee Madley brandished his second yellow despite the fact that replays would show he got the ball.
The draw represents a good return from a tricky fixture but Koeman was left frustrated that his side wasn't able to ride out the last 10 minutes to claim victory.