City have been fast starters over recent weeks but it was Everton who carved out the first opening when Dominic Calvert-Lewin broke away down the left.
His low cross found Andre Gomes but Bernard was deemed to have fouled Fernandinho in the box and Craig Pawson halted play.
City’s first opportunity fell to Leroy Sane after Everton had cleared a corner but the German could only volley wide of the far post.
Ayermic Laporte also had the chance to break the deadlock from their next corner, however, he powered his header wide from close range.
The chances continued to come for City as they settled into the game and Ilkay Gundogan struck the bar after latching on to David Silva’s cut back.
Silva was to play a key role in the opening goal in additional time at the end of the first half when his free kick found the head of Laporte.
This time the France international made no mistake as he looped it back across goal and beyond a despairing Jordan Pickford.
Clear cut chances were few and far between in the second period with City creating the only serious openings.
Sergio Aguero went close with a bicycle kick midway through the half after Pickford was beaten to a high ball by Bernardo Silva.
Everton saw more possession in the latter stages but were unable to test Ederson even after the introduction of Gylfi Sigurdsson and Richarlison.
The Citizens wrapped up the points in the last minute of additional time when two substitutes combined.
Kevin De Bruyne rolled the ball through for Gabriel Jesus who was denied initially by Pickford but looped the ball home at the second attempt.