Haaland's 18th-minute opener against Brugge saw him reach 15 Champions League goals in fewer games than any other player in the competition's history.
The 20-year-old Norwegian hit the milestone in just 12 appearances, smashing the previous record of 19 games held by Ruud van Nistelrooy and Roberto Soldado.
Haaland added another in the second half to take his tally to 16, as he and Dortmund annihilated Brugge to defend top spot in Group F and move within touching distance of qualification for the second round.
With two games to go, Lucien Favre's side are now five points clear of third place and a point ahead of second-placed Lazio, which beat Zenit Saint Petersburg 3-1 on Wednesday (AEDT).
Dortmund was predictably dominant in the first half, and it took Haaland just 70 seconds to send a shot fizzing past the Brugge post.
The Norwegian found the net on 18 minutes, placing a low shot past Simon Mignolet after Jadon Sancho set him up with an elegant through ball.
Sancho, who had been dropped to the bench for Dortmund's league win at Hertha Berlin last weekend, was in excellent form upon his return to the starting XI.
The 20-year-old Englishman doubled Dortmund's lead on the stroke of half-time, curling a free-kick into the top corner after compatriot Jude Bellingham was fouled on the edge of the box.
Haaland put the game beyond reach on the hour mark, gratefully pouncing on an inadvertent assist from Brugge midfielder Ruud Vormer and sweeping the ball in from close range.
-AFP
