Cliftonville have moved up to second in the Carling Premiership despite being held to a draw at Seaview.
Reds striker Diarmuid O'Carroll headed in the opener but poor defending let in Stephen O'Neill for the equaliser.
Liam Boyce restored the visitor's lead just before the break only for Carrick to level again when new signing Kyle Owens headed in at the backpost.
Philip Byrne made it 3-2 to Carrick on 88 but George McMullan equalised 60 seconds later with a backheel finish.
Cliftonville are six points adrift of leaders Linfield after squandering a series of chances to win this game.
Martin Donnelly hit the bar with an early free-kick and the Reds took a deserved lead when O'Carroll finished from a McMullan cross.
Boyce's first goal since his return to Solitude gave the north Belfast side a half-time advantage and Carrick's new keeper Paul Murphy kept the score at 2-1 with two saves to deny Stephen Garrett.
A Murphy mistake presented Barry Johnston with an open goal but the midfielder hammered over.
It proved to be a costly miss as Kyle netted before fellow new signing Byrne headed Rangers into a surprise lead from a corner.
The celebrations were shortlived with Cliftonville captain McMullan securing a point a minute from time.