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The Royal Blues of Gelsenkirchen are now unbeaten in their last four games including Thursday's 2-2 draw at Moenchengladbach which put them in the Europa League's quarter-finals on away goals.
Schalke's left-back Kolasinac capped a fine display with the decisive goal on 50 minutes.
The 23-year-old was wearing a mask after breaking his nose last month.
But he showed great vision to finish a move he started, swapping passes with striker Guido Burgstaller, then dribbling into the area and firing home.
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It was another good performance from Burgstaller who scored twice in last weekend's 3-0 win over Augsburg.
The 27-year-old's form since joining Schalke from Nuremberg in January has been rewarded with a call-up for the Austria squad for the forthcoming World Cup qualifier against Moldovia and friendly against Finland.
Schalke's second-half replacement Nabil Bentaleb could have added a second goal at the death when he broke free of the defence, but could not beat Mainz's Denmark goalkeeper Jonas Loessl.
It was an emotional return for Schalke's Mainz-born director of sport Christian Heidel.
It was his first appearance at the Opel Arena having started working for Mainz in 1992 before joining for Gelsenkirchen before the start of this season.