The on-loan Chelsea forward took his league tally for the campaign to six goals - just one fewer than he managed in 18 months at Stamford Bridge before being shipped out.
Batshuayi's latest strike, coming a week on from his dramatic double against Eintracht Frankfurt, was arguably his most audacious yet as he used the outside of his boot to flick the ball on for the only goal of the contest.
Three days on from their Europa League exit at the hands of Red Bull Salzburg, Dortmund started the match as though they had a point to prove.
The breakthrough moment arrived a little over a quarter of the way through, though, with Batshuayi diverting Schurrle's front-post delivery past Tschauner with a smart finish.
The Belgian striker perhaps should have added to his tally, missing a couple of openings from close range in the remainder, while up the other end Roman Burki was tested by Pirmin Schwegler from a rare Hannover chance.
Felix Klaus tried his luck with a couple of long-range efforts, but Dortmund looked comfortable and could have doubled their advantage when substitute Maximilian Philipp found the post rather than the back of the net late on.
BVB are now back within a point of second-placed rivals Schalke 04 in the race to finish runners-up behind Bayern Munich.
BORUSSIA DORTMUND (4-2-3-1): Burki; Piszczek, Akanji, Toprak (Sokratis 46'), Schmelzer; Castro (Weigl 64'), Dahoud; Pulisic (Philipp 70'), Gotze, Schurrle; Batshuayi
HANNOVER (3-4-1-2): Tschauner; Sorg (Fossum 78'), Anton, Sane; Korb, Schwegler, Bakalorz (Maina 86'), Ostrzolek; Klaus; Jonathas, Fullkrug (Sarenren Bazee 73')