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Kyle McVey headed the hosts into a 10th-minute lead and Tony Kane made it 2-0 with a penalty after Marc Smyth had pulled the shirt of Allan Jenkins.
Jay Donnelly volleyed past home keeper Alan Blayney and just before half-time Ballymena's Gavin Taggart was sent off after a clash with James Knowles.
A cool finish by Daniel Hughes brought Cliftonville level in the 82nd minute.
It was his first goal since joining the Belfast club from Warrenpoint Town in January.
New Sky Blues boss David Jeffrey remains undefeated since taking over from Glenn Ferguson with two draws and a win in the Premiership.
Cliftonville fought back from two goals down to draw with 10-man Ballymena United at the Showgrounds.