Dortmund, who host Shakhtar Donetsk for a spot in the Champions League last eight next week, were desperate for a confidence-boosting win that would simultaneously consolidate second place in the Bundesliga.
Bayern, who play lowly Hoffenheim on Sunday, lead the title race with 60 points with Dortmund on 46. Third-placed Bayer Leverkusen, on 42, host VfB Stuttgart later on Saturday.
Lewandowski, on the pitch only after he had his initial three-game suspension for a red card reduced to two matches late on Friday, fired the hosts into the lead from close range after a cutback from Kevin Grosskreutz.
The Poland forward, linked with a transfer to Bayern after refusing to extend his contract with the champions beyond 2014, added another in the 20th minute to go top of the league's scorers' list with 16.
Hanover, playing without injured midfielder Szabolcs Huszti and top striker Mame Diouf, pulled one back through Mohammed Abdellaoue just before the break but Julian Schieber killed any hopes of a comeback when he threaded in from 15 metres for his first goal of the campaign.
Schalke 04 teenager Julian Draxler scored twice and set up another goal as the Gelsenkirchen club continued their domestic recovery with a 4-1 demolition of VfL Wolfsburg for their second straight win.
Germany international Draxler struck either side of an Ivica Olic equaliser and then provided an assist to Peruvian Jefferson Farfan. Klaas-Jan Huntelaar drilled in from a tight angle in the 86th minute to help Schalke move up to sixth place on 36 points.
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- Champions League