Stuart King’s men were full of confidence following a win against Linfield in their previous outing, but were wary of the wounded animal that was Glenavon after they were defeated 5-1 by Newry City midweek.
The hosts grabbed an early foothold and after Eoin Bradley sent an effort past the post, they made the breakthrough courtesy of Matthew Fitzpatrick.
He latched onto a through ball and rounded Ross Glendinning to slot into an open goal.
However, the resilient Rangers hit back less than ten minutes later.
Andy Mitchell collected the ball 25 yards from goal and fired an outstanding strike over Rory Brown’s head to find the net, making it the second week running that the midfielder scored such a goal.
It would only take Glenavon a matter of minutes to regain their lead, though, as ex-Carrick player Conor McCloskey crossed for Bradley to bundle the ball over the line.
The game’s end-to-end nature continued as a long throw-in was turned onto the post by Carrick, with their opponents surviving the goalmouth scramble that followed.
It was all Rangers before the break as Emmett McGuckin flicked a header wide from a corner and Lloyd Anderson’s shot was blocked, but they found themselves behind at the break.
Fifteen minutes into the second half, Anderson broke through on goal only to be hauled down by Robbie Garrett.
Garrett was shown a straight red card and Carrick looked to make the most of their numerical advantage as Alex Gawne came off the bench for Reece Glendinning.
That swap would pay dividends immediately as Gawne’s cross to the back post, though looking like it was going just past Curtis Allen, was met by a remarkable overhead kick from the striker which flew past the helpless Brown to restore parity once more.
Allen could have grabbed his brace just after 70 minutes, but his side-footed shot from Ben Tilney’s pass went the wrong side of the post.
Despite being a man down, Glenavon were still in the game and substitute Matthew Snoddy perhaps should have done better when he saw his near post strike denied by Glendinning.
Anderson then flicked a header towards goal from a Tilney cross, but it was kept out by the chest of ‘keeper Brown who didn’t seem to know much about it.
McGuckin would have a final chance from a Kurtis Forsythe cross, but he header off target as the shares were spoiled between the sides.
Glenavon: Brown; Ward, Birney, Wallace, Glynn (Doyle, 68); McCloskey (O'Connor, 76), Baird, Garrett, Campbell (Carey, 32 (Doyle, 76)); Fitzpatrick, Bradley (Snoddy, 68).
Unused substitutes: Kerr, Scannell.
Carrick Rangers: Glendinning; Glendinning (Gawne, 63), Ervin, Gordon; Forsythe, Cushley (Cherry, 77), Mitchell, Tilney; Anderson; McGuckin, Allen.
Unused substitutes: Hogg, Kalla, McKiernan, Waite, Gillen.
Referee: Lee Tavinder