The Norwegian summer signing from Borussia Dortmund entered the contest at the Etihad Stadium having already scored a remarkable 34 goals in 35 appearances across all competitions in his debut campaign for the Citizens.
Haaland has now increased his goal tally in all tournaments to 39 following his five-star showing against Leipzig, which included a first-half hat-trick and two more strikes before the hour mark.
At the age of just 22 and 236 days, Haaland has become Man City's all-time record scorer in a single season, breaking the club's 94-year record set by Tommy Johnson back in the 1928-29 campaign when he netted 38 goals.
Haaland has also written his name in the Champions League history books, surpassing Kylian Mbappe (22 years and 352 days) as the youngest player to score 30 goals in the competition's history, while he also has reached the 30-goal landmark in the quickest time, doing so after just 25 games and surpassing the previous benchmark held by Ruud van Nistelrooy (34 matches).
In addition, Haaland has become just the third player to score five goals in a single Champions League game after former Shakhtar Donetsk striker Luiz Adriano in October 2014 (against BATE Borisov) and former Barcelona forward Lionel Messi in March 2012 (against Bayer Leverkusen).
Ilkay Gundogan and Kevin De Bruyne were also on the scoresheet to help the Citizens cruise into the Champions League quarter-finals with an 8-1 aggregate triumph over their German counterparts.
After drawing the first leg 1-1 at the Red Bull Arena three weeks ago, Pep Guardiola's side made a bright start to the second leg and Haaland converted the opening goal from the penalty spot in the 22nd minute after Benjamin Henrichs was deemed to have touched the ball with his outstretched right arm following a VAR review.
Haaland headed home a second just two minute later, pouncing on a loose ball after De Bruyne had rattled the crossbar with a venomous strike, and City's No.9 then completed his hat-trick on the stroke of half time when Amadou Haidara smacked his attempted clearance into the striker's shins after a Ruben Dias header hit the post and tricked across the goalline.
City's hunger to score more goals was evident and they came out the blocks quickly in the second half, with Gundogan stroking a sweet left-footed strike into the bottom corner three minutes after the break.
Haaland's fourth and fifth goals on the night soon followed, blasting home two similar strikes inside the penalty area within the space of four minutes just before the hour mark, before coming off to a rapturous applause in the 63rd minute.
De Bruyne then capped off an impressive performance with a stunning curling strike into the top corner from outside the area in added time, sealing City's joint-biggest Champions League victory.
Guardiola's side will look to extend their unbeaten run in all competitions to eight matches when they welcome Vincent Kompany's Burnley to the Etihad in the FA Cup quarter-finals on Saturday evening.