Third-placed Aston Villa are also not letting up in their title chase as they twice came from behind to win 3-2 at West Ham on Sunday.
Arsenal had extended their lead at the top of the standings to five points with an unconvincing 2-1 win against Wolves on Saturday.
But both their closest rivals responded impressively with second-placed City scoring a revenge win over the side that beat them to lift the FA Cup last season.
Haaland scored his 101st Premier League goal to put City in front late in the first half and finished the job in the 89th minute with their third goal from the penalty spot.
The Norwegian now has 36 goals in 27 appearances for club and country in another remarkable scoring season. He is the league's leading marksman with 17 goals.
In between his strikes, the influential Phil Foden got City's other goal as they moved on to 34 points from 16 games.
At the London Stadium, Morgan Rogers scored twice in the second half to extend Aston Villa's winning run to nine-straight games and keep Unai Emery's team on the heels of Arsenal and City.
Villa have lost just one of their last 13 games in the league, winning 10 of their last 11, but twice had to come from behind at relegation-battling West Ham.
Mateus Fernandes scored the fastest goal in England's top-flight this season when putting the home team 1-0 up after just 29 seconds, but an own goal from Konstantinos Mavropanos levelled the game eight minutes later.
Jarrod Bowen gave the home side the halftime lead in the 24th, but Rogers equalised again five minutes after the break and struck the winner in the 79th.
In the battle between the two sides who discarded Australian manager Ange Postecoglou, Nottingham Forest pulled further away from the relegation zone with a 3-0 win against Tottenham Hotspur.
The pressure's now mounting on Tottenham coach Thomas Frank after the latest loss, with Spurs having won just one of their last seven games in the league before they have to face defending champions Liverpool at home next week.
Two goals from Callum Hudson-Odoi at the City Ground put Frank's team on course for another defeat - a sixth in the league this season.
Ibrahim Sangare completed a miserable day for the visitors, but a joyous one for Forest, who are now five points clear of the relegation zone.
In the Tyne & Wear derby, Sunderland got the better of Newcastle 1-0 thanks to an own goal from Nick Woltemade.
The Germany striker Woltemade has impressed since his club-record move from Stuttgart in August, but he made himself a hero to Newcastle's fiercest rivals when he headed past Aaron Ramsdale and into his own net a minute into the second half.
To make matters worse, he was barely a threat at the other end - registering one shot before being replaced by Yoane Wissa in the 75th.
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