Group C remains wide open after Monaco grabbed a 1-0 win in Germany thanks to a second-half strike from substitute Lucas Ocampos.
Leverkusen dominated the first half, with Turkish midfielder Hakan Calhanoglu spurning several excellent chances to open the scoring.
However, it was Lars Bender who came closest to breaking the deadlock, but his powerful volley just before the half-hour mark came crashing back off the Monaco crossbar.
Giulio Donati's rifled shot was well blocked by Andrea Raggi minutes after the restart, before Calhanoglu's tame shot was easily saved by Danijel Subasic.
Referee Paolo Tagliavento then waved away Leverkusen's appeals for a penalty after Bender tumbled under the challenge of Raggi.
Roger Schmidt's side wasted their best chance to take the lead when Dimitar Berbatov gave the ball away to Josip Drmic just six yards out, but with only Subasic to beat Drmic dragged his shot wide.
Drmic's miss then came back to haunt Leverkusen as Monaco's Ocampos struck from close range with his first touch after coming on as a 70th minute substitute Yannick Ferreira-Carrasco.
The result means Leverkusen, Monaco and Zenit St Petersburg can all still qualify for the knockout stages.
