Borussia were then awarded a penalty on 32 minutes after Korb was bundled over in the box by Dennis Aogo.
Lars Stindl initial spot kick was kept out by Fahrmann, but the Schalke stopper was unable to stop the rebound as the midfielder atoned for this miss.
The visitors levelled, however, as Andreas Christensen put through his own net a minute before the interval.
Monchengladbach restored their lead with 20 minutes left after Raffael's free kick beat the dive of Fahrmann.
Schalke's hopes of getting a result suffered a further setback when Johannes Geis was sent off in the 80th minute.
Borussia then wrapped up victory moments later as Korb scored a third for the hosts, who are now just outside the European places.