The Germany international converted in just the fourth minute to seal the points, with Ron-Robert Zieler in the Hannover goal to thank for keeping the score close for the remainder.
After slumping to its first Bundesliga loss of the season before the international break with a 2-0 defeat to Borussia Monchengladbach, Dortmund was looking to bounce back immediately at Signal Iduna Park, and included Sokratis Papastathopoulos in place of the suspended Mats Hummels in the heart of defense.
Dortmund started at a frightening pace, and won a penalty within three minutes as neat interplay tore Hannover's defense open and full back Erik Durm was felled by Hiroki Sakai.
Reus made no mistake with the spot kick, firing into the top corner for his fifth league goal of the season.
On 13 minutes, Hannover looked to hit back with its only clear chance of the first half but Artur Sobiech's left-footed strike was saved comfortably by Roman Weidenfeller in goal.
Dortmund continued to press relentlessly, with Henrikh Mkhitaryan at the heart of its good play. The Armenian set up chances for Reus and Kevin Grosskreutz, but they could not find a way past Zieler.
The goalkeeper was again called into action just past the half-hour, comfortably saving Reus' free-kick to his right to keep Hannover within reach at the break.
The away side came out for the second half with a renewed confidence and went close on 51 minutes through the dangerous Sobiech, but the striker steered over the bar from a Szabolcs Huszti cross.
In an open start to the second half, Lewandowski forced Zieler into a smart stop on 55 minutes with a fierce left-footed drive as the hosts continued to be frustrated.
With the game still tight, Hannover almost spoiled the party for Dortmund and saw two attempts from Edgar Prib and Deniz Kadah both rebuffed by the hosts.
The game finished as lively as it had started with 90th-minute substitute Julian Schieber almost finding Lewandowski in the box in the dying moments but the game finished just in Dortmund's favor, Jurgen Klopp's side remaining a point behind table-topper Bayern Munich.
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