Phil Foden and Ruben Diaz also scored against Sevilla for City, who got off to a dismal start to five defeats in six games.
City coach Pep Guardiola said of Haaland, who scored goals for RB Salzburg and Dortmund in the Champions League: “I think all the numbers in his career are very similar, even with his previous teams.” .
“He has an incredible sense of purpose.
Foden twisted and turned in the box to extend City’s lead before Haaland scored a second, while Diaz slammed Joao Cancelo’s drill cross to complete the rout in stoppage time.
The defeat left Sevilla 17th in La Liga with one point from four games and the worst start to the club’s history as fans called on club president Pepe Castro to step down.
That leaves City and Dortmund, who face each other in Manchester next week, as the two teams most likely to qualify for the knockout stage.