Jordan Stewart's late equaliser secured a point for Glentoran at Solitude.
Joe Gormley found the net with a precise finish over the head of Elliott Morris for his 32nd goal of the season.
Danny McKee twice went close to levelling, with Stephen Gordon also going close, while Gormley flashed a header narrowly wide for the Reds.
Stewart flicked the ball over a defender and toe-poked past goalkeeper Peter Cherrie when the ball landed back at his feet in the final minute.
Cliftonville are now without a win in six league matches as their defence of the title continues to stutter.
After the prolific Gormley broke the deadlock in the 18th minute, Stewart headed the ball across goal, but McKee saw his fine 10-yard volley blocked on the goal-line by George McMullan.
McMullan supplied the delivery for Gormley, who could have extended the home side's advantage, but his header went just off-target.
After half-time, McKee's header was acrobatically flicked over by Cherrie, then Jude Winchester's stinging shot had Morris back-pedalling.
Cherrie made a terrific save from Gordon with his feet, and produced another fine stop from the dangerous McKee.
Morris denied Sean McCarron and last week's League Cup final hero, Martin Donnelly, fired over.
The Glens earned just reward for their efforts with that late well-taken strike by the impressive Stewart.
Cliftonville manager Tommy Breslin: "That match sums up the last six or seven weeks when we've got ourselves into decent positions but haven't been able to turn them into victories.
"As each game goes by, that plays on the players' confidence and mindset."
Glentoran manager Eddie Patterson: "There were a few harsh words said to certain individuals at half-time and we came out and played better after the break.
"I though the equaliser wasn't going to come, but I think we deserved it for our second half performance."