Pep Guardiola's side capitalised on the defeats suffered by closest rivals Bayer Leverkusen and Borussia Dortmund on Saturday, stretching their unbeaten run to 47 games in the German top flight.
Hannover offered some spirited early resistance at the HDI Arena but fell behind after 25 minutes through Thomas Muller's 10th league goal of the season, a powerful header that proved too strong and accurate for Ron-Robert Zieler.
Thiago Alcantara added the second in the first half, while Muller rounded off an impressive display by completing his double just before the hour and Mario Mandzukic deservedly added a fourth with 24 minutes remaining, nodding in Rafinha's cross.
The result extends Bayern's winning streak in the league to 14 games, while Hannover saw their four-match unbeaten home run come to an end.
Bayern coach Guardiola rested some key players following the 2-0 UEFA Champions League win at Arsenal, as Arjen Robben, Toni Kroos and Manuel Neuer dropped to the bench, while Franck Ribery missed out altogether.
The visitors unsurprisingly dominated possession early on, but it was Hannover who created the first meaningful chance.
Artjoms Rudnevs collected Szabolcs Huszti's throughball and surged past Tom Starke, but the goalkeeper recovered to make an important block.
Bayern broke the deadlock with their first real opening midway through the half, Rafinha delivering a pinpoint cross from the right for the unmarked Muller to head home.
Zieler was called into action twice in quick succession just after the half-hour mark as he produced good saves from Mario Mandzukic and Mario Gotze, but he was powerless three minutes later.
Bastian Schweinsteiger played a brilliant lofted pass into the area for Thiago, and the former Barcelona man confidently controlled the ball before smashing past Zieler.
Bayern put the result beyond doubt with 59 minutes gone as Mandzukic flicked on David Alaba's left-wing cross for Muller to convert.
Mandzukic added the fourth when Rafinha fired in another teasing cross from the right and the Croatian rose highest to head in.
Christian Schulz went close to grabbing a late consolation for the hosts as his half-volley was deflected agonisingly wide of the left post, but Bayern ultimately held on to their clean sheet.
