Mario Goetze scored the winner on the hour-mark to give Dortmund its first victory in four league games and keep the side three points ahead of his former club Bayern Munich, which had moved level with a 1-0 win over Hertha Berlin on Saturday.
Leverkusen had been on a four-game winning run under new coach Peter Bosz, who was fired by Dortmund in December 2017.
Dortmund, which was leading the Bundesliga by nine points at one stage, was without a win in five games across all competitions.
Eintracht Frankfurt won 3-0 at Hannover in the earlier game.
Source: Fox Sports