VfB Stuttgart moved out of the relegation zone when substitute Sven Schipplock snatched an 88th-minute goal as they beat St Pauli 2-1 in the day's other game.
Mainz were playing the ball out of defence from a goal-kick when Renato Augusto, running back after taking a corner, stole it off Bo Svensson in the 82nd minute.
The Brazilian advanced before whacking a curling shot past goalkeeper Christian Wetklo from 20 metres, leaving Mainz's perplexed defenders looking at each other in disbelief.
"It was very important for us to win especially after losing that Europa League match to Villarreal," said goalkeeper Rene Adler whose Leverkusen side lost 3-2 at home to the Spaniards on Thursday.
Vidal blasted his effort over the bar after being found free on the left and Kiessling shot tamely at Wetklo after being sent clear of the defence by the former Flamengo player's chipped pass.
At the other end Andrea Schuerrle wasted Mainz's best chance by firing high and wide from a Christian Fuchs cross.
Fabian Boll put St Pauli ahead after 19 minutes but Zdravko Kuzmanovic levelled five minutes later. Schipplock had only been on the field for five minutes when he grabbed the winner for Bruno Labbadia's team.
