Latvian Artjoms Rudnevs and South Korea international Son Heung-min scored twice each as Hamburg inflicted the first defeat for Dortmund after four straight wins, with both teams left with 10 men in the second half.
The results could mean leaders Bayern Munich, on 51 points, extend their gap to a staggering 15 if they beat out-of-form Schalke 04 later on Saturday, with Dortmund second on 39 points and Leverkusen a point behind in third.
Werder Bremen beat VfB Stuttgart 4-1 with the hosts left licking their wounds after their fifth straight defeat that adds pressure on coach Bruno Labbadia, who only last month extended his deal to 2015.
VfL Wolfsburg climbed further away from the relegation zone with a 1-0 victory over bottom-placed Greuther Fuerth thanks to Bas Dost's eighth goal of the campaign to move up to 12th on 26 points.
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