City can clinch their spot in the knockout stage when they play Young Boys again, this time at home, on Nov. 7.
Haaland scored for the first time in six Champions League games with a penalty in the 67th minute after Mohamed Camara's tackle on Rodri in the box.
Haaland, who rewrote several scoring records last season, added another one on Wednesday, breaking Kylian Mbappe's mark as the youngest player to score 37 Champions League goals.
But Young Boys caught City keeper Ederson in no man's land to level four minutes later, sending in Meschack Elia with a superb pass which he scooped high over Ederson into the net.
Young Boys are third in the group on one point after three matches.
Persons:
Erling Haaland, Manuel Akanji, Pep, Guardiola, I'm, Haaland, Mohamed Camara's, Akanji, Ruben Dias's, Anthony Racioppi, Meschack Elia, Jack Grealish's, Racioppi, Matheus Nunes, Loris Benito, Rico Lewis, City's Julian Alvarez, Grealish, Lori Ewing, Clare Fallon
Organizations:
Manchester City, Champions League, Swiss, Young Boys, Wednesday, TNT Sports, League, Boys, Ederson, Thomson
Locations:
Norwegian, Swiss