The winning goal came after Schalke goalkeeper Timo Hildebrand rolled the ball to a defender and they broke quickly down the left hand side.
An exchange of passes ended with Raffael slipping the ball between three defenders for Draxler, 19, to fired past Marc-Andre Ter Stegen for his ninth goal of the league season.
Schalke, who are fourth in the Champions League playoff spot, have 52 points from 32 games, four behind third-placed Bayer Leverkusen and six ahead of Eintracht Frankfurt in fifth.
"It's not over yet, we still have two very difficult games to go," Schalke 04 coach Jens Keller told Sky.
"A draw might have been a fairer result but we were lucky enough to get a late goal, the two teams cancelled each other out."
Seventh-placed Gladbach, who have managed only seven goals in their last 11 league games, twice hit the woodwork early in the second half.
Granit Xhaka curled one effort against the crossbar and midfielder Juan Arango hit the foot of the post.
Gladbach could slip to ninth if results this weekend go against them. The defeat also rules them out of the hunt for a Champions League place, although they can still qualify for the Europa League.