Everton survived the dismissal of Steven Pienaar and a strong late penalty appeal from City to hand Manchester United the opportunity to go 15 points clear at the top of the table by beating Reading later.
City were incensed when referee Lee Probert awarded a free-kick rather than a penalty despite an apparent hand-ball in the box by Everton’s Marouane Fellaini when the visitors trailed 1-0.
City assistant coach David Platt said manager Roberto Mancini was too “angry” to speak to media after the game and claimed his side had been denied a blatant spot-kick.
“You’ve just played it to me (on a television replay) and it’s not even on the line of the area, it’s three yards inside,” he told Sky Sports.
“People can draw their own conclusions, but we didn’t get it. Perhaps we could have got more out of the game if the decisions had gone for us.”
Leon Osman made the breakthrough for the hosts in the 32nd minute, meeting Seamus Coleman’s lay-off with a swerving shot from 25 yards that deceived goalkeeper Joe Hart and flew into the top-left corner.
Pienaar was sent off with half an hour to play following a shin-high foul on Javi Garcia, but second-choice Everton goalkeeper Jan Mucha kept the visitors at bay with fine saves to thwart Carlos Tevez, James Milner and Pablo Zabaleta.
Substitute Nikica Jelavic curled in Everton’s second goal in injury time to seal a win that banished memories of last weekend’s abject loss to Wigan Athletic in the FA Cup.
“We have had one or two dips but that was more like us today,” said Everton manager David Moyes.
“I thought we had a bad performance last week, which the fans rightly reminded us about, but we just reminded them they are supporting a really good team.”
Victory temporarily lifted Everton into fifth place, but they slipped back to sixth after Arsenal won 2-0 at Swansea City to move to within two points of fourth-place Chelsea.
January signing Nacho Monreal and Gervinho struck late in the game at the Liberty Stadium as Arsene Wenger’s side responded in positive fashion to their mid-week elimination from the Champions League.
Meanwhile, Liverpool lost ground in the race for European qualification after losing 3-1 at Southampton.
Morgan Schneiderlin neatly converted a Jay Rodriguez knock-down in the sixth minute to put Southampton ahead at St Mary’s, before Rickie Lambert doubled the hosts’ lead with a deflected free-kick.
Philippe Coutinho replied for Liverpool on the stroke of half-time, but Rodriguez made sure of victory in the 80th minute as Mauricio Pochettino’s side pulled seven points clear of the relegation places.
Queens Park Rangers were left seven points adrift of safety at the foot of the table after losing 3-2 to relegation rivals Aston Villa in a thrilling encounter at Villa Park.
After Jermaine Jenas gave QPR an early lead, Villa hit back through Gabriel Agbonlahor and Andreas Weimann, only for Andros Townsend’s deflected strike to draw the visitors level in the 73rd minute.
However, there was a further twist in the tale, as Christian Benteke stroked home the winning goal from Weimann’s cut-back with nine minutes remaining.
Benteke’s goal allowed Villa to put six points between themselves and the bottom three, although third-bottom Wigan have two games in hand.
In the day’s other game, Stoke City failed to reverse their disappointing recent form in a goalless draw at home to West Bromwich Albion.