Crawley Town chief coach Dermot Drummy was relieved to get the final point which kept Reds in League 2.
Reds let slip a two-goal lead courtesy of a James Collins brace which were cancelled out by strikes at the other end by Jabo Ibehre and Jamie Proctor.
In the second half Carlisle went 3-2 up on the hour-mark through Reggie Lambe and it looked like Crawley were on their way to a home defeat.
Finally in the third minute of added-time captain Jimmy Smith scored the third goal which brought them the point they were looking for.
The result combined with Hartlepool United's 2-0 defeat at home by Barnet to keep Crawley seven points clear of the relegation zone with two matches to go, meaning they are safe from the drop.
Drummy praised both the fans and the players for giving one final push which led to Smith scoring to earn them the draw they needed to stay up.
The Reds boss believed his third substitution when he brought on Jordan Roberts in place of Kaby Djalo, was the catalyst which led to Crawley's all-important third goal.
Drummy said: "Their third goal was calamitous, the crowd was anxious and the pressure's on.
"I thought bringing Jordan (Roberts) on and changing the system, we got deliveries in and we got bodies forward with more purpose rather than just the long ball.
"You've got to give credit to the players and the fans for deciding we've got to suck this goal in.
"The fans were getting on it and you want that every game.
"It's a nice relief maintaining the status but on the flipside I came here with hopes of the play-offs.
"But when you look at this division and the journey you go on and look at the dips in form and you look at the big clubs which stay in there - to keep our status is an achievement."