Goals from Joe Thompson and Matt Done put Dale ahead in the second half after Carlisle took the lead through Marcus Holness` own goal.
But a 30-yard stunner from Liam Noble and goalkeeping error from Owain Fon Williams from Matty Robson`s free-kick completed the turnaround.
"I thought this performance was one of the best of the season from us when you consider we were playing a team desperate for points," said Abbott. "We had to replicate their honesty and application and did that, and it was a contest between two well-matched teams. If we'd come here with the wrong attitude we would have been beaten.
"It's a terrific win for us and the only disappointing thing is that Rochdale suffer from it and they have a hard task now to keep their season alive. I admire what Keith Hill and David Flitcroft are doing here and it's nice to see clubs like this, with limited resources, doing really well. But it is my job to win games.
"The big difference on the day was the two wonder strikes from long range in the second half and we were fortunate enough on the day to have the players in the right positions to hit them as they did, and that ultimately won us the game."
Source: PA
Source: PA