The trainer drew level with Matthias Sammer on the club's all-time wins list as the defending champions earned a narrow victory against last season's runners-up
The result was a personal milestone for Jurgen Klopp, who recorded his 68th victory at BVB, drawing him level with Matthias Sammer as the second-most successful coach in club history.
The game began like a tactical chess match, but at the end of the first half, Shinji Kagawa broke the deadlock following a brilliant bit of personal skill. And while Leverkusen remained within striking distance of a point to the very end, BVB held strong and never looked like conceding.
Neither side could create much space in attack for long spells in the first half, but Kagawa capitalised on poor defending from Manuel Friedrich, skilfully touching the ball past the centre-back before beating Bernd Leno from a tight angle.
Before the opener, Kevin Grosskreutz had a clear chance to put the hosts ahead on 30 minutes as Vedran Corluka nodded the ball directly to his feet, but the Germany international fired straight at Leno.
At the other end, Stefan Kiessling almost opened the scoring, but Lukasz Piszczek did well to close the gap and block his attempt from close range. Gonzalo Castro nearly found the net directly from an early corner, but Roman Weidenfeller recovered to tip over the bar.
Scoring chances again were at a premium in the second half, even after Robin Dutt introduced attackers Renato Augusto (61st minute) and Karim Bellarabi (75th minute) for the more defensive Simon Rolfes and Corluka, respectively.
Leno was quick off his line to deny Robert Lewandowski on 48 minutes, and Neven Subotic had a free kick sail narrowly wide after an hour. Arguably the best chance of the half came on 64 minutes as Kagawa played Grosskreutz through on goal, but the Germany international again failed to find the net with only Leno to beat.
The only Leverkusen player to have even a sniff at goal in the second half was Kiessling, but the striker shot at the wrong target. The former Nurnberg man's defensive header on 69 minutes flew directly towards the top-left corner of Leno's goal, but the shot stopper did extremely well to make a catch-save.
Leverkusen managed to keep the game close until the very end, but in spite of Dutt's replacements and the need for a goal, could not put anything together in the attacking third, and succumbed to defeat.
The result sees Leverkusen remain sixth but fall a further point behind Werder Bremen, who drew with Hoffenheim. Dortmund remain atop the table, two points ahead of Bayern Munich.