The Citizens were made to work for their three points against a spirited Young Boys outfit, but goals from Haaland (2) and Manuel Akanji ultimately ensured that the reigning European champions preserved their perfect start in Group G.
After a goalless first half, Akanji opened the scoring three minutes after the break with a close-range finish on his return to his native Switzerland, before Meschak Elia restored parity for the hosts just four minutes later with a lofted finish over Ederson.
However, Haaland put Man City back in front from the penalty spot, slotting his effort from 12 yards down the middle, before curling a fabulous right-footed finish into the top corner four minutes from time to seal the win for Pep Guardiola's side.
Man City are on the cusp of booking their place into the Champions League knockout rounds as they already sit at the summit of Group G and five points above both Young Boys and Red Star Belgrade in third and fourth respectively, while RB Leipzig are three points adrift in second place.
At the age of just 23 years and 96 days, Haaland has become the youngest-ever player to score 37 goals in the Champions League.
The Norwegian has broken the record previously held by Paris Saint-Germain star Mbappe, who reached 37 goals at the age of 23 years and 295 days.
Haaland has ended a run of five matches and 543 minutes without a goal in the Champions League to achieve this feat, with his penalty goal against Young Boys his first in the competition since finding the net in a quarter-final second-leg draw at Bayern Munich in the middle of April.
Man City's No.9 has remarkably scored his 37 Champions League goals in just 33 games, including 14 goals in as many matches for the Citizens, 15 goals in 13 games for Borussia Dortmund and eight goals in six appearances for Red Bull Salzburg.
Haaland won the Champions League Golden Boot award last season after netting 12 times in 11 games, and his brace against Young Boys has put him in contention to retain the individual accolade this term at this early stage, as he sits just a goal behind seven names including teammate Julian Alvarez and Real Madrid's Jude Bellingham.
Since making his professional debut at club level in 2016, Haaland has been directly involved in 115 goals in his last 100 appearances across all competitions, scoring 96 goals and registering 19 assists.
Sixty-three of those goals have been scored in 67 games for Man City, with his latest brace moving him onto 11 goals in 14 appearances across all tournaments this season.
Haaland could have scored more against Young Boys while he has had a few dry spells in front of goal so far this season, leading to somewhat bizarre criticism from small sections of the football community, but Guardiola believes that those critiquing the striker just want him to "fail".
Asked in an post-match interview with TNT Sports whether Haaland is worried about missing chances, Guardiola sarcastically replied: "A lot, a lot. I am so concerned. Honestly I'm so concerned."
The Catalan boss then added: "It is important to have the chances, the people want him to fail. I am sorry but this guy will score goals all his life, with the chances he is an incredible threat.
"The players need the ability to find the pass like Kevin De Bruyne and Ilkay Gundogan. But he is going to score until the last day he plays football."
Haaland will look to increase his goal tally when Man City travel to Old Trafford to lock horns with rivals Manchester United - who the Norwegian scored three times against last season - in the Premier League on Sunday.