The home victory allows Dortmund to peg back the points gap behind Bayern, who remain on course for a 10th straight league title after thumping Stuttgart 5-0 on Tuesday.
Haaland has scored 19 goals in 15 games for Dortmund this season and the towering Norwegian again shone at Signal Iduna Park.
His early well-timed pass in the box saw Thorgan Hazard hit the net, but the goal was ruled offside.
Dortmund are also six points ahead of third-placed Leverkusen, who were held to a 2-2 draw at home by Hoffenheim on Wednesday.
Czech striker Patrik Schick scored twice to put Leverkusen 2-0 up with an hour gone, but Hoffenheim scored late goals from Angelo Stiller and Munas Dabbur to claim a point.
Leverkusen finished with ten men after Moussa Diaby was shown a second yellow card for lashing out at Hoffenheim defender Florian Grillitsch in stoppage time.