Mario Mandzukic was involved in Bayern's two first-half goals, heading on for Mario Gotze to drive into the left corner for the opener after 11 minutes and then making a nuisance of himself in the box before Franck Ribery fired in the second just before half-time.
Arjen Robben and Dante scored in quick succession midway through the second half, and Mandzukic snagged the fifth goal in the 88th minute as Bayern stretched an unbeaten record that now stands at 44 Bundesliga games.
Bayer Leverkusen, who sit in second place despite already losing five games this season, had briefly made up ground on Bayern with victory over Stuttgart on Saturday.
Earlier on Sunday, Nurnberg made it two wins out of two in 2014 with a 3-1 victory at Hertha Berlin.
Josip Drmic scored twice for the Bavarians, taking him on to 10 goals for the season and four in two games, but the hosts were left fuming by a decision which denied them an equaliser late on.
Adrian Ramos gave Hertha the lead before Markus Feulner levelled and Drmic put the visitors in front, but the real drama was reserved for the final few minutes when Hertha were first awarded a penalty only to see the referee change his mind.
The official then gave the Bavarians a penalty, from which Drmic wrapped up the win.