After Lucas Alario secured an early lead for the home side, Bayern struck twice in quick succession just before half-time to turn the game in their favour after Kingsley Coman’s equaliser.
Lewandowski netted in the second half as Bayern established a 10-point lead over title rivals Borussia Dortmund, who host Hertha Berlin later on Saturday.
The game also saw Bayern lend their support to protests over the death of black American man George Floyd, with all their players wearing armbands bearing the slogan “Black Lives Matter”.
With their talisman and Bayern transfer target Kai Havertz ruled out with a muscle injury, Leverkusen turned to Alario to lead the line against the champions.
The Argentine delivered after just nine minutes, beating the offside trap after a throw-in to slot the ball past Manuel Neuer.
A mistake from Moussa Diaby allowed Coman to curl in the equaliser, before a fizzing shot from Leon Goretzka and an elegant lob from Serge Gnabry saw Bayern take a two-goal lead before half-time.
Lewandowski finished the job with a well-placed header after the break, reaching the 30-goal mark for only the second time in his Bundesliga career, but there was still time for 17-year-old Florian Wirtz to curl in a consolation goal for Leverkusen before the final whistle.
Elsewhere, a late equaliser from Christian Strohdiek gave bottom-of-the-table Paderborn a faint glimmer of hope in the race for survival, as they snatched a 1-1 draw away to RB Leipzig.
Chelsea-bound Leipzig striker Timo Werner set up Patrik Schick on 27 minutes to give Leipzig the lead, but they were forced to defend it with 10 men after Dayot Upamecano was booked twice in the first half.
Strohdiek’s last-minute strike gave Paderborn their fourth draw in five games, though Steffen Baumgart’s side remain eight points off Fortuna Duesseldorf who occupy the relegation play-off place.
Duesseldorf themselves missed the chance to move towards safety, as they battled to a dramatic 2-2 draw against 10-man Hoffenheim.
A headed opener from Rouwen Hennings and a red card for Hoffenheim’s Benjamin Huebner put the home side in pole position, but the visitors struck back with goals from Munas Dabbur and Steven Zuber before Hennings saved a point with a late penalty.
Uwe Roesler’s side remain three points adrift of survival, after goals from Moussa Niakhate and Pierre Kunde Malong gave fellow strugglers Mainz a rare 2-0 win over local rivals Eintracht Frankfurt.