Dortmund scored on the stroke of half-time when Japan international Shinji Kagawa shook off two defenders with a fine solo run and slotted the ball home with a clever left-foot shot from a tight angle.
The champions, who have won all four of their Bundesliga games this year without injured playmaker Mario Gotze, are now unbeaten in 15 straight league games since early September.
"I am very satisfied with the way we played because I knew it would be hard," Dortmund coach Jurgen Klopp told reporters. "Leverkusen were very organised and worked hard but we put in a solid home performance against a tough-defending opponent."
"We have confirmed our upward trend," said Bayern coach Jupp Heynckes, whose team started with winger Arjen Robben on the bench for the second consecutive game.
"It was a fully deserved win. We again kept a clean sheet. I am especially satisfied with the way we defended."
Mid-table VfB Stuttgart crushed 10-man Hertha Berlin 5-0 with four goals in a 17-minute spell in the first half to put visiting coach Michael Skibbe under more pressure after his team's fifth defeat in his five games in charge.
Hoffenheim's new coach Markus Babbel, sacked by Hertha in December, thought he would celebrate a winning debut until Werder Bremen's Marko Arnautovic snatched a 90th-minute goal to earn his side a 1-1 draw.
Hannover 96 also had to wait until the end to spoil Mainz 05's afternoon with Artur Sobiech equalising in the 89th minute to secure a 1-1 draw.
