Germany international Kevin Grosskreutz twice took advantage of poor defending to score in the 49th and 53rd minutes and Mario Goetze added another in the 55th to give visiting Dortmund their 15th win in 18 league games.
Leverkusen, who had captain Michael Ballack on the bench after more than four months out injured, pulled one back through Stefan Kiessling 10 minutes from time.
Jurgen Klopp's team, who avenged their season-opening defeat by Bayer, have 46 points, 13 ahead of second-placed Mainz 05 and Leverkusen.
"These were big points for us," said a delighted Klopp who earlier this week brushed aside suggestions Dortmund could struggle with the pressure in the second half of the season.
"We picked up where we left off and fully deserved the win but it is still going to be hard for us," he told reporters.
