Haaland's league-leading 23rd goal of the campaign in the 65th minute on Sunday (Monday AEST) allowed City to trim the gap to Arsenal, the long-time frontrunners, to just three points.
City have a game in hand at Burnley on Wednesday, after which Pep Guardiola's team could have taken over as leaders.
Rayan Cherki gave City the lead in the 16th minute of a frenetic match at Etihad Stadium by weaving into the area and converting a shot in off the inside of the post.
But Arsenal were back level inside two minutes after Kai Havertz capitalised on a shocking error from goalkeeper Gianluigi Donnarumma, who carelessly delayed his clearance, with the ball rebounding into the net from close range off the German international.
Both Haaland and Arsenal's Eberechi Eze struck the goal frame before the Norwegian superstar slotted home a low shot from Nico O'Reilly's cross, dealing a huge blow to Arsenal's hopes of a first league championship since 2004.
City are expected to beat struggling Burnley, but they do have a tougher-looking run-in than Arsenal, including trips to Everton and Bournemouth.
But unlike City, who are unbeaten in 10 league games, Arsenal are struggling for form, having now lost four of their last six games in all competitions — including their last two in the league.
Mikel Arteta's team, runners-up for the past three seasons, also have to balance playing in the Champions League after reaching the semi-finals.
Elsewhere, Liverpool and Aston Villa look to be headed for the Champions League after grabbing stoppage-time winners.
Virgil van Dijk headed home from a corner in the 10th minute of added-on time to earn Liverpool a 2-1 victory at Everton in a Merseyside derby featuring a record-tying goal from Mohamed Salah.
Salah, who is leaving Liverpool at the end of the season after nine trophy-filled seasons, marked his final derby by slotting in a low finish in the 29th minute. His ninth Merseyside derby goal drew him even with Liverpool great Steven Gerrard for the most in the Premier League era (since 1992).
Villa, meanwhile, beat Sunderland 4-3 thanks to Tammy Abraham's goal in the third minute of stoppage time.
Fourth-placed Villa moved 10 points ahead of sixth-placed Chelsea, with Liverpool between them, but stretched their advantage over Chelsea to seven points.
At the other end of the table, Morgan Gibbs-White scored a second-half hat-trick in the space of 15 minutes as Nottingham Forest rallied to beat Burnley 4-1 and further boost their survival hopes.
Forest moved five points clear of third-to-last Tottenham in the relegation zone, while next-to-last Burnley also slipped closer to the drop to the Championship.
