The Addicks were determined to bounce back after suffering their first defeat of the League One campaign at Stevenage last week and made the perfect start by taking the lead in the 14th minute at The Valley on Saturday.
Rhoys Wiggins swung in a cross from the left and Kermogant's header gave visiting goalkeeper Adam Collin no chance.
A mistake by James Tavernier from Ben Hamer's long clearance was capitalised on by Bradley Wright-Phillips seven minutes later as the Addicks striker fired past Collin to double the advantage.
Kermogant added his second in the 37th minute after Wright-Phillips had seen two efforts cleared off the goalline and Carlisle were reduced to 10 men a minute before the break when Matt Robson picked up his second yellow card for a trip on Wright-Phillips.
Danny Hollands' long-range strike three minutes into the second half went straight through the legs of Collin to make it 4-0 and Carlisle squandered a great chance to grab a consolation after Michael Morrison was adjudged to have handled in the penalty area, but James Berrett's 56th-minute penalty was saved by Hamer.