Two late goals consigned Stanley to a fourth successive league defeat as Carlisle celebrated a Boxing Day victory.
The Cumbrians took an early lead through ex-Red loan winger Jamie Devitt before Billy Kee made it 13 for the season from the penalty spot just after the re-start.
However sub Shaun Miller struck on 78 minutes and captain Danny Grainger made it safe as John Coleman’s men dropped out of the play-off places.
Stanley enjoyed a lot of the early possession with Liam Nolan blasting their first real effort over the bar on ten minutes.
Carlisle opened the scoring a minute later when Hallam Hope flicked the ball on for Devitt – on loan at Stanley in 2012 – to fire home from a tight angle.
Stanley continued to pass the ball around but their next shot didn’t come until the 30th minute when Sean McConville tested keeper Jack Bonham for the first time.
The Cumbrians went on the hunt for number two with Aaron Chapman getting a hand to the ball before Hope could get a free shot on goal while Devitt fired straight into the keeper’s arms from distance.
Grainger hit the side netting from a free kick and Devitt should have doubled the advantage on 36 minutes as he was free six yards out but he blasted over the goal.
Mallik Wilks had a great chance to equalise before the break when a short back pass let him in one-on-one with Bonham but the keeper denied him with his feet.
Stanley did level two minutes after the restart when Tom Parkes fouled Kayden Jackson in the area and Kee scored his second penalty in two games to make it 1-1.
Carlisle still looked dangerous and Chapman turned a Parkes header onto the bar while Hope blasted a six-yard shot well over the bar to the relief of the visiting fans.
The game was end-to-end with Jackson hitting the top of the bar with a strike on the hour mark as Stanley were much-improved after the interval.
The home side retook the lead 12 minutes from time with former Morecambe striker Miller making something out of nothing, turning and volleying low into the bottom of the net.
Carlisle went on the hunt for the third with Mike Jones hitting the woodwork and then they secured the three points with Grainger firing home the third seven minutes from time after Hope’s strike was blocked.