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Stefan Kiessling would prove to be a constant threat for Leverkusen in attack as Karius was twice forced to make good saves to keep out the striker early in the game.
Kiessling's frustration would continue as Karius raced off his line to get a strong hand on his low effort after a long ball had split the Mainz defence.
Neither side looked dangerous in attacking areas early in the second half as the defenders enjoyed superiority at the BayArena.
A clever run from Kiessling saw him break free of the Mainz defence on the hour mark, but he was thwarted once again as Karius tipped a shot past the post.
Hakan Calhanoglu was the next player to test the reflexes of Karius, who continued his man-of-the-match display by blocking his close-range strike.
After surviving an extended spell of Leverkusen pressure, Mainz should have opened the scoring from Malli's free kick, but Shinji Okazaki could only head wide of the target from an inviting position in the box.
Inevitably, it was Karius who made one final vital contribution late on by pushing Calhanoglu's swerving effort to safety.