Haaland put City back into the lead on the artificial surface at Bern’s Wankdorf Stadium after Switzerland international Manuel Akanji’s opener had been brilliantly cancelled out by Meschack Elia.
Substitute Julian Alvarez had an effort ruled out by VAR but Haaland made victory certain with a smart finish four minutes from time.
The win was City’s third in succession in Group G and they could now secure their spot in their last 16 for an 11th successive year with a follow-up victory over the Swiss side at home in a fortnight.
There had been much talk over the synthetic pitch in the build-up to the game and heavy rain added another variable element but it proved a free-flowing encounter.
Young Boys started well with Filip Ugrinic forcing a save from Ederson before Rodri headed wide from a corner.
Jack Grealish, who ignored the persistent booing of the vociferous home crowd, teed up Jeremy Doku with a superb first-time ball but the Belgian slipped as he cut inside and Anthony Racioppi saved.
The impressive Swiss keeper denied Haaland soon after but did have a moment of alarm when he spilled a Grealish shot. Matheus Nunes could only poke the loose ball weakly towards goal, however, and Loris Benito cleared off the line.
Doku went close again after switching from the right to left wing but Racioppi brilliantly saved his curling effort and blocked a first-time Rodri shot.
Young Boys had a good spell before the break with first Cedric Itten breaking clear but failing to beat Ederson.
Itten then teed up Sandro Lauper with a neat flick but Nathan Ake got back to block before a powerful Lewin Blum effort was turned behind. Itten went close again from the set-piece as his header dropped narrowly over.
While that made for a lively end to the first half, the game truly burst into life early in the second.
Akanji and Nunes both had chances before City grabbed the lead in the 48th minute. Rodri delivered a cross into the box and Ruben Dias, still forward following a corner, had a header tipped onto the bar by Racioppi. Akanji reacted the quickest to turn the ball in.
City went in immediate search of a second but were caught out after a Haaland shot was saved by Racioppi.
The ball was quickly sent to the other end and played into the path of Elia, who caught Ederson stranded off his line with a superb lob.
Young Boys were firmly back in the game and Itten forced Ederson into an awkward save with a swerving shot.
City stepped up the intensity and were awarded a penalty when Mohamed Ali Camara, moments after being booked, caught Rodri from behind. Haaland stepped up to thump home his 10th of the season.
City thought they had claimed another through Alvarez but his low strike was ruled out for a Grealish handball in the build-up.
It fell to Haaland to complete the job, the striker wrong-footing the defence just inside the box and then lifting into the top corner.