Both sides had decent chances early on. Boro striker Oumare Tounkara outmuscled Sean O'Hanlon but could only scuff wide off balance before Lee Miller headed a Conor Townsend cross straight at Stevenage goalkeeper Chris Day.
Carlisle skipper Miller was a constant threat and was rewarded after in the 27th minute when Matty Robson's shot was blocked on the line brilliantly by Peter Hartley, allowing Miller to stab home the rebound.
The home side drew level in the 58th minute when Luke Freeman was tripped in the box by Troy Archibald-Henville and Greg Tansey stepped up to slot home from the penalty spot.
But two late goals put the game to bed as Robson fired home with a left-footed drive with 13 minutes to go before former Liverpool man David Amoo struck with five minutes to go after substitute David Symington hit the post.