Tom Nichols marked his competitive return to The People's Pension Stadium with a 32nd minute goal to give the Reds a half-time lead.
Jon Mellish levelled with seven minutes of normal time remaining before Tsaroulla thumped the ball home to seal the three points for Crawley.
The victory lifts John Yems' side up to 19th in League Two.
Here are Coren Blackburn's player ratings for the day.
1. Glenn Morris - 7
Always a safe pair of hands. Wasn’t too busy thanks to how well his back four defended, but was still reliable when called upon. Photo: Steve Robards
2. George Francomb - 7
Led a new-look back four very well and helped his team get through a difficult spell of Carlisle pressure in the second-half. Played his part in a solid defensive display from the Reds. Photo: Steve Robards
3. Tom Dallison - 7
Defended well in the centre-back position alongside Joel Lynch and battled well against Tristan Abrahams, nullifying the usually dangerous forward. Photo: Pete Norton/Getty Images
4. Joel Lynch - 9
A fantastic debut, aerially imperious and tidy in possession. No clean sheet on his debut, but an important three points and a man of the match award. Photo: Crawley Town FC