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Hours after Arsenal's 3-0 win over Bournemouth, Pep Guardiola's men responded with a resounding victory that pulled them to within a point of the North Londoners at the top of the standings, but with a game in hand.
Mikel Arteta's side moved into first place with 68 points from 30 games although Liverpool, who have 67, can move back to the summit with a home game against Sheffield United.
Manchester United fanned the embers of their top-four hopes with a 2-0 win against visiting Everton.
Liverpool have 60 points with champions City on 59 and Arsenal on 58, all three teams having played 26 games.
Uruguayan Nunez put the seal on a dominant Liverpool display with his second goal in stoppage time.
Manchester City slipped out of the top four as Tottenham Hotspur made up ground with a third consecutive victory, beating Everton 2-1 at home.
The Portuguese manager spent four seasons at Wolves and helped get them promoted to the Premier League in his first season there.
Leon Bailey's deflected strike after a surging run in the 74th minute sealed Villa's club record-equalling 14th successive home league win as they moved above City into third place.
Ten-man Chelsea beat Brighton & Hove Albion 3-2 at Stamford Bridge while fourth-placed Aston Villa needed a late Ollie Watkins goal to scrape a 2-2 draw at Bournemouth.
Anthony Gordon scored the only goal in Newcastle's deserved 1-0 victory over Manchester United that propelled them up to fifth in the table on 26 points.