The teenager's second-half strike secured a point after Mario Gotze's emphatic penalty had given the reigning Bundesliga champion a deserved halftime lead.
The 19-year-old's strike midway through the second half cancelled out Mario Gotze's penalty as the 2012 champions failed to capitalize on a dominant opening period.
The visitors, who were without top scorer Robert Lewandowski, failed to pose enough of a threat going forward despite having the majority of possession and are now 17 points behind leaders Bayern Munich at the top of the table.
After an even start, Dortmund went close to opening the scoring inside 10 minutes as Kevin Grosskreutz saw his effort saved by Marco-Andre ter Stegen after Moritz Leitner headed Mats Hummels' cross into his path on the edge of the six yard box.
Without the suspended Lewandowski, the visitors were struggling to make an impact in the final third, though ter Stegen was forced into a save from Leitner's powerful header.
Gotze was the man tasked with filling Lewandowski's boots in the forward position, and he made his first meaningful contribution of the game as he took the ball around ter Stegen before being tripped by the goalkeeper.
The referee rightly pointed to the spot and Gotze brushed himself down before sending the goalkeeper the wrong way and give Jurgen Klopp's side a deserved lead.
The home side was struggling to get a foothold in the game, and it continued to come under pressure as Hummels and Ilkay Gundogan both shot off target while Leitner fired a long range effort straight at ter Stegen.
Hummels was withdrawn at halftime due to injury, and his replacement Felipe Santana almost handed the hosts an equalizer as his weak clearance only found Younes, but the teenager's volleyed effort failed to stretch Roman Weidenfeller.
Gladbach was gradually coming back into the match, and Weidenfeller was forced to tip Harvard Nordtveit's cross over the bar, with the resulting corner falling to Martin Stranzl, but his free header from close range was straight at the goalkeeper.
Lucien Favre's side eventually found the goal that its improved performance deserved as it attacked down the left, and after Oscar Wendt's cross was only half cleared, Younes fired home from the edge of the area via a deflection off Santana.
Despite conceding, Dortmund was still a threat going forward, and after winning the ball back inside the hosts' box, Gotze fired into the side netting, though a measured cross may have been better advised.
Germany international Gotze was by far the visitors' main threat, and he tested ter Stegen with a powerful strike after working his way into a shooting position. The goalkeeper was equal to it, though, pulling off an acrobatic save.
Gladbach almost pulled off an unlikely victory in the final minute of normal time as substitute Peniel Kokou Mlapa broke the offside trap and rounded Weidenfeller but could only find the side netting from a tight angle.
That wasn't the end of the drama as Gotze made his way past two defenders before laying the ball across goal, only for Sebastian Kehl to sum up his side's day by firing over the bar with the goal gaping.