Dortmund scored all of their goals inside the first 32 minutes as they overwhelmed their hosts with some incisive attacking play.
The German side top the table midway through the pool stage with six points from three matches, one ahead of second-placed Lazio, who were held 1-1 at Zenit St Petersburg earlier on Wednesday. Brugge are third with four points.
Haaland missed the weekend's Bundesliga victory at Arminia Bielefeld with a knee injury, but showed no ill-effects as all his predatory instincts were on display to take his goals tally at Dortmund to 26 in 28 games since he joined the club in January.
The visitors looked the more dangerous side from the start and secured a deserved opener when Brugge goalkeeper Simon Mignolet could only palm a Thomas Delaney cross into the path of Hazard. Mignolet had a chance to redeem himself but let the resulting shot burst through his hands.
Dortmund added to their tally four minutes later as Mignolet could only parry Haaland's close-range header and the striker turned in the rebound.
The Bundesliga side kept pressing forward and Haaland bagged his brace after former Brugge right-back Thomas Meunier raced in behind the home defence and laid the ball off for a tap-in and a fourth goal in his three Champions League games this season.
Dortmund coach Lucien Favre will be pleased with the comfortable manner of the win as they prepare for a clash with domestic title rivals Bayern Munich on Saturday.