Leon Bailey fired them into the lead with a 20-metre missile three minutes after the restart with the sensational 20-year-old Jamaican taking his goal tally to eight this season.
Wendell added another with a penalty in the 68th as Leverkusen equalled a club record of having scored in their last 25 consecutive Bundesliga matches.
Argentine Lucas Alario should have grabbed a late goal but keeper Robin Zentner kicked his bouncing close-range header wide.
The result lifted them to second place and 34 points, as many as third-placed Schalke 04, and one point ahead of Eintracht Frankfurt.
Leverkusen have now lost just once in their last 15 league games.
Bayern Munich are on track for a record-extending sixth consecutive Bundesliga title after coming from 2-0 down to crush Hoffenheim 5-2 on Saturday to stay 16 points clear at the top on 50.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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