Monchengladbach were among the early title challengers in the German top flight but their campaign was dealt another blow with a potentially costly defeat to one of their main rivals for a European spot.
Schalke have now leapfrogged Monchengladbach into third after Swiss midfielder Barnetta gained the crucial goal in a close-fought contest.
Boateng crossed for Barnetta, who timed his run perfectly to finish past Yann Sommer.
While Monchengladbach huffed and puffed, Lucien Favre's men failed to break down a resolute Schalke side shorn of suspended striker Klaas-Jan Huntelaar.
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