The defending champions wasted no time in exploiting Dortmund's inexperienced defence, with Nathan Tella scoring just 25 seconds into the game. Patrik Schick then doubled the lead on the eight-minute mark with a clinical finish.
English winger Jamie Gittens pulled one back but Schick restored Leverkusen's two-goal lead shortly afterwards.
A late Serhou Guirassy penalty gave Dortmund hope but Leverkusen held on for their ninth straight win in all competitions, turning up the heat on Bayern, who travel to Borussia Moenchengladbach on Saturday.
"I'll be honest, we're not looking at Bayern, we're focused on ourselves and we're on the right track," Leverkusen's Granit Xhaka told DAZN.
Leverkusen coach Xabi Alonso benched in-form midfielder Florian Wirtz due to an "internal issue".
Dortmund's problems were less vague, with three first-choice centre-backs along with wing-backs Pascal Gross and Bensebaini missing.
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Dortmund's makeshift defence, including youngsters Almugera Kabar and Yannik Luehrs, was breached almost immediately.
England-born Nigeria winger Tella unleashed a superb strike into the top corner after Leverkusen pressed the nervous hosts into a mistake while playing out from the back.
The visitors quickly doubled their lead, Schick tapping in Piero Hincapie's low cross.
Dortmund dragged themselves back into the match just four minutes later when Gittens chipped in after Robert Andrich inadvertently poked the ball into his path.
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Schick however added his second and Leverkusen's third on the 19-minute mark, this time diverting in a cross from the right.
"I expect my lads to defend better than that, even with the situation we have in defence," Dortmund coach Nuri Sahin said.
Schick, who started the season on the bench behind Victor Boniface, now has 11 goals in his past six league appearances.
"I work hard every day. I was of course ready when the chance came," Schick said.
"I want to give the max for the team and I'm happy I could help out with a couple of goals."
With 11 minutes remaining, VAR awarded Leverkusen a penalty and Guirassy converted nervelessly from the spot to give the home side a shot at snatching an unlikely point, but Leverkusen held firm.
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Champions League finalists last season, Dortmund have won just one of their past five Bundesliga fixtures and could finish the weekend as low as 10th.
(Except for the headline, this story has not been edited by staff and is published from a syndicated feed.)