Raphael Wicky mentioned before kickoff that his team had "nothing to lose" and claimed they were capable of beating the defending champions to earn their first win in the competition this season.
Pep Guardiola, on the other hand, was looking forward to a third consecutive win in Europe which would see his side take a solid lead in the group and allow him to rest a few players until the knockout stages.
It was a lively start to the match, and both teams got early sights of goal with attempts by Filip Ugrinic and Rodri at either end inside the first five minutes, though neither were able to stick away the half-chances they were afforded.
City began to control the match as the half wore on, generating opportunities but falling short when it came to converting them, with Haaland and Jeremy Doku both missing presentable chances.
The visitors were almost gifted the lead before half time when Jack Grealish fired a tame shot at Anthony Racioppi, who fumbled the ball onto Matheus Nunes, but Loris Benito got back to clear off the line and kept the scores level at the break.
Guardiola was noticeably frustrated heading down the tunnel with his side bossing the game with 75% possession, recording 10 shots at goal and six on target, but still without a goal to show for their first-half dominance, while YB were still in the game and looking dangerous in transition.
However, the City boss did not have to wait long for a reason to crack a smile, as his side came flying out the blocks in the second period and got their reward with Akanji tapping in a rebound from a Ruben Dias header to give his side the lead and register his first-ever goal for The Citizens.
The hosts levelled proceedings less than five minutes later, though, with an early ball over the top that found Meschak Elia, who put a glorious chip over Ederson and into the corner of the net.
As the game went on, there was a growing feeling that it was just a matter of time until City regained the lead, and they did just that as Rodri was brought down in the box and Haaland stepped up to slot away the spot kick.
The Citizens thought they took the game out of sight in the 74th minute when Julian Alvarez played a quick one-two with Haaland before rolling home, but the goal was ruled out for a handball on Grealish in the build-up.
It was mostly one-way traffic from then on, with the champions dominating possession and despite being denied on numerous occasions from open play throughout the 90 minutes, Haaland got his second of the night five minutes before time with a delightful curling shot from inside the box.
City have won their group in the Champions League in the last six seasons and look well on their way to the knockout stages again this term.
Young Boys will be back in league action this weekend against Lugano, while Manchester City will face their cross-town rivals in the Manchester Derby on Sunday.