Bayern, who took the lead with a Joshua Kimmich goal after only 62 seconds, oozed new-found confidence as they rode roughshod over the hosts.
They fired 13 shots on goal compared to their opponents' single effort in the first half and David Alaba doubled their lead with a 29th-minute missile from 20 metres.
In the absence of their veteran wingers -- Arjen Robben was injured and Franck Ribery rested -- 22-year-old Kingsley Coman and Serge Gnabry terrorised the Hanover defence with their speed.
Gnabry made it 3-0 in the 53rd and Robert Lewandowski headed in their fourth goal in the 62nd as the hosts capitulated.
"The team played really well over 90 minutes, created many chances and the result should have been higher," said Bayern coach Niko Kovac, whose position looked in doubt only a few weeks ago with his team in sixth at that point.
Bayern also finished top of their Champions League group after their midweek 3-3 draw at Ajax Amsterdam.
"It was good to see the team take the Bundesliga very seriously after such a hard game at Ajax. We did our homework and were dominant. I can feel we are turning the corner," said Kovac.
Bayern, who have put last month's dip in form behind them two matchdays before the start of the winter break, moved on to 30 points, third on goal difference behind Borussia Moenchengladbach, who drew 0-0 at Hoffenheim.
Leaders Dortmund are on 39 after beating Werder Bremen 2-1 for their sixth straight league win.
Mario Gomez scored twice for VfB Stuttgart to help them beat Hertha Berlin 2-1 but the victory was overshadowed by the sudden death of the father of Stuttgart captain Christian Gentner in the stadium immediately after the game.
(Reporting by Karolos Grohmann; Editing by Ian Chadband and Clare Fallon)
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