Germany international Reus, plagued by injuries for much of the season, drilled the ball home in the 41st minute and set up Henrikh Mkhitaryan for the second goal nine minutes later.
Gladbach, in fourth place, cut the deficit with a fine low drive from Raffael but Armenia international Mkhitaryan then delivered a pin-point assist for Ilkay Guendogan to score after a quick break in the 75th minute.
Dortmund, on 41 points, stayed eight behind leaders Bayern Munich, who beat Hamburg SV 2-1 on Friday, and moved eight clear of third-placed Hertha Berlin who drew 0-0 against Augsburg on Saturday.
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VfB Stuttgart fought back from a goal down to beat Cologne 3-1, picking up where they left off before the winter break and claiming a second successive win that lifted them out of the relegation zone.
Daniel Didavi and Timo Werner struck either side of the break after Anthony Modeste's 19th-minute penalty had put the hosts ahead.
Captain Christian Gentner made it 3-1 in the 84th minute to leave Stuttgart 14th on 18 points.
New Hanover 96 striker Hugo Almeida scored on his comeback to the Bundesliga after a five-year absence but visiting Darmstadt 98 rallied to snatch a 2-1 triumph at the bottom club thanks to two goals from Sandro Wagner.
It was a losing debut for Hanover coach Thomas Schaaf who took over during the winter break.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
