In the 27th minute, Hoffenheim's Steven Zuber missed a penalty and, ten minutes later, Quaison was very close to giving his team the lead as his free kick screwed into the post and then rolled a few inches from the goal line.
Instead, Hoffenheim took the lead with two minutes left of the first half through Ilhas Bebou.
In the second half, Mainz pushed for better, but the match ended 1-0 and they are now just one point from relegation.