After midfielder Toni Kroos put the hosts ahead at Munich’s Allianz Arena with a well-taken first-half chip, Germany striker Mario Gomez extended his tally as the Bundesliga’s top scorer with his 23rd goal in 26 matches.
He rolled his shot under Hanover goalkeeper Ron-Robert Zieler on 68 minutes to claim Bayern’s second before Ivory Coast striker Didier Ya Konan pulled a goal back with a spectacular bicycle kick on 74 minutes.
Hanover could have rescued a point as ex-Manchester United striker Mame Diouf headed over the bar with time almost up.
With Dortmund at Cologne on Sunday in the Rhineland derby, Bayern took the opportunity to cut the defending champions lead, leaving them on 57 points to the Dortmund’s 59 with seven matches left.
Third-placed Borussia Moechengladbach slipped further back in the title race when they threw away the lead to lose 2-1 at home to Hoffenheim, which leaves them six points behind Bayern, eight behind Dortmund.
Gladbach were cruising to victory after a first-half goal from Dortmund-bound midfielder Marco Reus seven minutes before half-time but Hoffenheim took the three points with two goals in as many second-half minutes.
Brazil midfielder Roberto Firmino earned a yellow card for his shirtless celebrations on 77 minutes before a sharp header from Boris Vukcevic on 79 minutes scuppered Gladbach’s hopes.
Schalke 04, who host Leverkusen on Saturday night, can now claim third place if they beat Robin Dutt’s team in Gelsenkirchen.
Kaiserslautern coach Krassimir Balakov, who took over after Marco Kurz was sacked in midweek, had an unhappy start to his tenure as his team were beaten 2-0 at Freiburg to remain bottom of the league.
It was Kaiserslautern’s 17th league game without a win and means they are now six points adrift at the bottom.
Slovakia’s Karim Guede put his side ahead after only eight minutes before Freiburg captain and Congo international Cedrick Makiadi added the second with a header on 14 minutes.
The win lifts Freiburg to 14th and drops Hamburg into the relegation places after they lost 2-1 to Wolfsburg on Friday night.
Hertha Berlin remain second from bottom despite their 3-1 win at Mainz but things are tight at the bottom as only two points separate 17th and 13th in the league.
Hamburg’s chairman has backed coach Thorsten Fink to keep them away from relegation despite the German league club’s fourth consecutive defeat saw them slip into the bottom three.
“I’m still convinced that we have the right coaching staff,” said Carl-Edgar Jarchow on Saturday after a meeting with Fink.