London - Chelsea midfielder Willian broke through Everton's resistance with a late goal to clinch a 1-0 over the 10-man visitors on Wednesday and preserve the team's seven-point lead at the top of the Premier League.
Willian's 89th-minute strike from outside the penalty area flew past goalkeeper Tim Howard. It came shortly after Everton midfielder Gareth Barry was sent off for fouling Willian and receiving a second yellow card.
In the same melee, Branislav Ivanovic avoided any sanction for an apparent attempted headbutt on James McCarthy.
Winning was all the more important for Chelsea given City, which is second in the table, routed Stoke 4-1 at the same time.
Chelsea had been repeatedly frustrated by Howard on the American's return to action after almost seven weeks out with a calf injury, including tipping over Willian's first-half shot.
After the break Howard blocked Eden Hazard's effort from a tight angle, tipped Nemanja Matic's free kick clear and produced a low diving save to thwart Willian.
Chelsea manager Jose Mourinho used the game to rotate the squad, with goalkeeper Petr Cech coming in for Thibaut Courtois and producing a quick reaction save to keep out a second-half shot from former Blues striker Romelu Lukaku.
Everton is 12th in the standings.