Kingsley Coman’s deflected strike doubled the lead, before Leroy Sane headed home to make it three just two minutes after Bayern’s Marc Roca was sent off.
Mergim Berisha slotted past Manuel Neuer for Salzburg’s consolation.
The reigning European champions have won all four of their Group A games.
Lewandowski is now level with Raul as the joint-third top scorer in the competition’s history, behind only Lionel Messi (118) and Cristiano Ronaldo (131).
He opened the scoring for the German champions with a close-range finish, before Coman’s shot from 25 yards took a huge deflection off Maximilian Wober for the second. Sane’s headed third came just six minutes after he came off the bench to replace Serge Gnabry.
Roca was shown a second yellow card on his Champions League debut leaving Bayern with 10 men for 24 minutes.
Austrian champions Salzburg were dominant for much of the first half and had chances to go ahead, but remain without a win in this season’s Champions League and bottom of the group.
Elsewhere in Group A, Atletico Madrid drew 0-0 with Lokomotiv Moscow, allowing Bayern to pull seven points clear at the top.