The Belgian broke the deadlock with a clever tap-in from a Julian Brandt pass in the 72nd minute just after coming on with Dortmund struggling against the second division's bottom club.
Another Brandt cross found Hazard at the far post nine minutes later and he slotted the ball home once more to make sure of their spot in the next round of the competition.
In a lacklustre first half, Dortmund's Jude Bellingham had their best chance when the England international hit the crossbar with a superb shot from outside the box.
There was little else of note in terms of attacks, with striker Erling Haaland out with a hip flexor injury and Dortmund coach Marco Rose initially opting to rest several of his key players, including Hazard and captain Marco Reus.
However, the hosts should have scored seven minutes after the restart when forward Steffen Tigges somehow sent his header against the crossbar from three metres out before Reus and Hazard were brought on to liven up their attacking play.
Hazard combined with Reus and Brandt a minute after coming on to put Dortmund in front and then made sure there would be no Cup upset at the Signal Iduna Park with his second goal.
Fellow Bundesliga clubs Hertha Berlin and RB Leipzig also progressed by beating Preussen Muenster 3-1 and Babelsberg 1-0 respectively.
German champions Bayern Munich are in action at Borussia Moenchengladbach on Wednesday.