Rivals Bayern Munich moved into second place on 48 points from 23 matches after beating Schalke 04 2-0 with Frenchman Franck Ribery grabbing both goals in a dazzling performance.
Poland international Lewandowski fired in from a tight angle in the first half as hosts Dortmund initially attacked at will with Hannover's busy schedule including Europa League matches looking to have sapped their energy.
The 23-year-old then took his league tally to 16 goals, sliding in 10 minutes after the restart for his second.
Substitute Didier Ya Konan cut the deficit on the hour for the visitors but Dortmund's Ivan Perisic struck in stoppage time to extend the hosts' unbeaten run to 17 games and lift them to 52 points.
"We played a very good game and it was only down to us that we did not decide it in our favour much earlier," said Dortmund coach Jurgen Klopp.
Earlier on Sunday Ribery scored twice as home side Bayern bounced back from their 1-0 Champions League midweek defeat at Basel to move back into second spot.
"We are back in the game," Ribery, who combined well with fellow winger Arjen Robben throughout, told reporters. "We showed a good reaction. Now we have to keep winning and wait for Dortmund to slip up."
Bayern coach Jupp Heynckes opted to bench playmaker Toni Kroos and instead deploy Thomas Muller in a central role between Ribery and Robben as he reshuffled the team in search of more offensive spark.
The gamble paid off as the trio were a constant threat to the Schalke defence.
Former Germany keeper Timo Hildebrand was on hand to deny Robben and Muller before racing out of goal nine minutes from the break to stop Ribery and instead seeing the ball float over his head as the Frenchman snatched the lead.
Schalke's Joel Matip should have levelled right after the restart when he was sent through with only goalkeeper Manuel Neuer to beat but instead fired wide.
Bayern punished the visitors with Ribery combining well with Muller in the box to grab his 10th league goal as Bayern looked sharper than in their last five league games where they had taken only two wins.
The victory lifted Bayern back into second place, a point ahead of third-placed Borussia Monchengladbach, who drew 1-1 with Hamburg SV on Friday. Schalke remain fourth on 44.
