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.
5. Nick Tsaroulla - 8
Fantastic. Brilliant going forward, controlled and ran with the ball so well. Caught out in the build up to the equaliser but more than made up for it with an absolute stunner to win the game.
Photo: Simon Dack/Telephoto Images
6. Jack Powell - 8
Worked well with Payne and Hessenthaler, providing the quality to start attacks for Crawley. Was on the end of a painful challenge from Jack Armer, with the Carlisle left-back escaping with only a yellow.
Photo: Steve Robards
7. Jake Hessenthaler - 7
Battled against a good Carlisle midfield and came out on top. Took part in a running battle with Jon Mellish, and was up for the fight.
Photo: Pete Norton/Getty Images
8. Jack Payne - 7
A consistent performer in a Crawley shirt. Always eager to win the ball and looked to find the runs of Ashley Nadesan and Kwesi Appiah in the second-half.
Photo: Jamie Evans/UK Sports Images Ltd