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.
The pivotal moment came 10 minutes in when the visitors surrendered possession deep in their own half, with the ball worked out to Kevin-Prince Boateng on the right.
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.
Alexia Putellas: "We’re already the only club to have won the men’s and women’s Champions League, so the only thing even more historic to do than that would be to win it in the same season"
‘Trent has won everything he can for Liverpool, but of those who’ve left that we wanted to stay, who’s actually done better? I can only come up with one’: Reds legend highlights potential danger of Alexander-Arnold moving to Real Madrid
