The form suggested an away win with Mainz winless in four and Wolfsburg having won their last three in the league, but the hosts were handed the initiative after just 13 minutes when Draxler was shown a straight red card for a high foot on Gonzalo Jara.
That dismissal was the only incident of note in a quiet opening half an hour characterised by battles in the midfield and an absence of scoring chances, but with 13 minutes left of the half Mainz capitalised on their numerical advantage.
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After Daniel Caligiuri's shot was blocked for Wolfsburg, the home side countered with pace and Diego Benaglio could only parry Jairo Samperio's effort into the path of Pablo de Blasis for the midfielder to score.
The second half continued in disjointed fashion as the 10 men of Wolfsburg struggled to find a way back into the match, and they nearly fell two behind when Yunus Malli fired wide from the centre of the box.
It was 2-0 with 15 minutes remaining, however, as Malli swivelled to fire home his seventh goal of the season and double Mainz's advantage and secure a first win since October 4.