Wednesday's (Thursday AEST) result condemned American-owned Burnley to relegation after one season back in the top flight.
Haaland ran onto Jeremy Doku's pass to convert a deft finish in the fifth minute, allowing City to back up their 2-1 victory over Arsenal on Sunday that, for many, turned Pep Guardiola's team into the title favourites.
However, with goal difference potentially coming into play, City might regret not putting more past Burnley at Turf Moor.
City ended the night having had 28 attempts at goal, but could not find a second strike when they had hoped for several.
Winning by a one-goal margin left them and Arsenal tied on both points (70) and goal difference (+37). City only lead courtesy of more goals scored (66 to Arsenal's 63).
City were nine points adrift of the Gunners after drawing with West Ham United on March 14. Three straight wins, combined with back-to-back losses for Arsenal, has seen the title race turn on its head.
Mikel Arteta's side can return to the top of the pile when they host Newcastle United on Saturday with City in FA Cup semi-final action against Southampton but it is, at least for now, advantage City, who have lost just one of their last 21 league games.
At the Vitality Stadium, substitute Sean Longstaff volleyed a last-gasp equaliser as Leeds United edged closer to safety by twice coming from behind to dent Bournemouth's European push with a 2-2 draw.
Ahead of Sunday's FA Cup semi against Chelsea, Daniel Farke's side moved on to 40 points – nine clear of the relegation zone – after Longstaff lashed home in the seventh minute of added time.
Bournemouth were seconds away from climbing to sixth place following an 86th-minute goal from Rayan after James Hill's own goal cancelled out Junior Kroupi's opener.
With PA.
