Nicolas Maurice-Belay scored what was to prove the winner in the 73rd, with a low drive into the bottom left corner.
"I had a bit of a feeling before he hit it but I didn't know if it was a good one or not," Carrasso said about the saved penalty. "But I said to myself, 'if you want to be fourth tonight, you have to save the penalty.'
"I concentrated a lot then I made my decision and it was a good one. Often when a penalty is saved people say that it wasn't hit well, but I still stopped it."
Bordeaux moved provisionally into fourth place, nine points behind third-place Lille. Valenciennes is five points from safety.
Lille was looking to recover from a 1-0 defeat at Bordeaux, which had ended a run of three successive wins and 11 clean sheets.
Bastia had not won at Lille since 1996 but went in front in the third minute when Ludovic Genest, who was making his first Ligue 1 appearance in more than six years, controlled the ball on his chest and volleyed home from 25 meters.
But Lille took the lead thanks to two goals in three minutes from Salomon Kalou, who had not scored in 757 minutes.
The Ivory Coast striker grabbed his first in the 19th minute, collecting the ball from Nolan Roux before switching feet to round Bastia defender Sebastien Squillaci and fire into the far corner.
Kalou doubled his tally with a curling shot in under the bar and thought he had a hat trick shortly before halftime but it was harshly ruled out for offside.
"It was about time I scored, it had been a bit long," Kalou said. "When you are a striker, it annoys you when your team wins and you don't score. I never doubted myself but it started to play in my mind a bit. But I also had the help of my teammates and the coach always showed me he had confidence in me."
Marseille is 11 points behind Lille after its remarkable comeback.
Lyon had won only one of its past four league matches but took the lead in the 17th minute when Alexandre Lacazette was given too much space to collect Yoann Gourcuff's pass and wrongfoot Marseille goalkeeper Steve Mandanda.
Bafetimbi Gomis doubled Lyon's lead two minutes from halftime after being unselfishly set up by Henri Bedimo but Andre-Pierre Gignac reduced the deficit in first-half stoppage time with a powerful strike from 30 meters.
Marseille leveled in somewhat fortunate circumstances in the 79th minute when Florian Thauvin's free kick was deflected over goalkeeper Remi Vercoutre by both Bedimo and Lacazette in the Lyon wall.
"Gignac's goal completely changed the match," Marseille interim coach Jose Anigo said. "There was a positive reaction in the dressing room. That shows the state of mind that we're getting into. In any case, it's an important point. We couldn't win this match, so it meant we mustn't lose."