The defending champions produced yet another dominant performance to make it 50 games unbeaten in the Bundesliga and move 23 points clear at the top following Borussia Dortmund's 2-1 loss against Borussia Monchengladbach earlier in the day.
In the week that president Uli Hoeness resigned after being jailed for tax evasion, Bayern provided the perfect tonic on the pitch and took the lead on 44 minutes through Croatian striker Mario Mandzukic.
Leverkusen - whose 2-1 success at the Allianz Arena in October 2012 marked the last time Bayern lost a Bundesliga game - had provided stern resistance up to that point, but from there on Sami Hyypia's men easily succumbed to defeat, which was ensured early in the second half thanks to Bastian Schweinsteiger's superb free-kick.
Stefan Kiessling did score a 91st-minute consolation for Leverkusen late on, but Pep Guardiola's men will now secure the title for a record 24th time if they beat Mainz next weekend and Dortmund and Schalke both fail to win.
Bayern made six changes to the side that drew with Arsenal in the UEFA Champions League in midweek, with winger Franck Ribery left on the bench by Guardiola.
Both teams traded chances early on, Arjen Robben drawing a fine low save from Bernd Leno after eight minutes, before Son Heung-Min missed a glaring opportunity to give Leverkusen a shock lead two minutes later.
The South Korean striker was slipped through by Kiessling, but sent his close-range shot narrowly wide of the post.
Defences were on top for much of the first half and only the fine reflexes of goalkeeper Manuel Neuer kept Bayern on level terms as he produced an excellent stop to tip Simon Rolfes' long-range drive over the bar.
But for all for their attacking initiative, Leverkusen were undone shortly before half-time as Mandzukic glanced Schweinsteiger's right-wing cross into the top corner.
And victory was all but ensured for Guardiola's men 10 minutes after the break when Schweinsteiger curled a marvellous free-kick beyond a despairing Leno.
Bayern refused to take their foot off the gas and pushed on for a third, which would have arrived if not for Leno, whose diving save kept out a powerful Toni Kroos strike from distance.
Leverkusen pulled one back in injury time as Kiessling headed home from Roberto Hilbert's right-wing cross, but that proved to be little more than a footnote as Bayern moved within touching distance of the title.
