Vincent Janssen had a goal disallowed and later hit the bar, while Erik Lamela's rising shot was tipped over by goalkeeper Bernd Leno as we pressed forward impressively in the opening 45 minutes at the BayArena.
But the introduction of Julian Baumgartlinger by Leverkusen boss Roger Schmidt at the break completely changed the hosts' dynamic and they played us at our own game from then on, closing the ball down quickly and denying us any real time on the ball.
In the end, a stunning save from Hugo Lloris - something akin to a combat roll across his own goal-line - to deny Leverkusen hotshot Javier Hernandez proved crucial as the game ended without score and the points were shared.