The Ruhr valley club, whose goalkeeper Ralf Faehrmann was in outstanding form with a string of key saves, moved past Gladbach into the fourth and final Champions League qualifying berth on 44 points, leaving the visitors two points behind in fifth.
Gladbach had enough gilt-edged chances to secure victory but they were either denied by Faehrmann, who was again overlooked for a Germany call-up earlier on Friday, or missed the target.
A slapstick Gladbach own goal gave the hosts the lead on the hour, with Martin Hinteregger sending the ball into his own net after an inadvertent pinball exchange with team mate Havard Nordtveit after a Leroy Sane cutback.
It was Austria international Hinteregger's second own goal in nine matches for the Foals.
Mahmoud Dahoud almost pulled the visitors level with a thundering 20-metre effort that bounced off the bar before Andreas Christensen equalised in the 79th minute.
However, a wicked deflection four minutes later gave Schalke an unexpected win with Granit Xhaka turning his back on Goretzka whose shot skidded off the back of the Swiss international for the winner.
Leaders Bayern Munich, on 66 points, visit Cologne on Saturday (1430 GMT), with second-placed Borussia Dortmund, on 61, travelling to Augsburg on Sunday (1630 GMT).
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
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