Without top goalscorer Erling Haaland through injury, captain Reus settled any Dortmund nerves in aftermath of the 5-2 thrashing at the hands of Bayer Leverkusen last time out, drilling the visitors in front in the 18th minute.
Reus then put Dortmund firmly in command in the capital seven minutes later, after rounding the goalkeeper and slotting home the second.
Having remained in control for the majority of the second half, Raphael Guerreiro poked home a late third to make sure of the win for the visitors.
Bayern’s shock 4-2 defeat by VfL Bochum on Saturday opened the door for second-placed Dortmund, who took full advantage to keep the title race alive on 46 points from 22 matches played, six points off the champions.
This season’s surprise package Union never really got going, with a second successive defeat meaning they drop to sixth in the table.
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