Neither side were able to convert the numerous chances they created in an entertaining draw at Ballycastle Road.
Chris Curran was twice denied in the first half by Michael Doherty, who also saved well from Jay Donnelly and Stephen Garrett's 25-yard shot.
Darren McCauley forced Peter Burke into a fine stop while Martin Donnelly had a shot cannon off the post.
James McLaughlin fired across the face of goal and straight at Burke, with McCauley having a header ruled out.
McCauley found the net in the second half but the referee blew up for an infringement.
Cliftonville remain third in the table, one point ahead of fourth-placed Coleraine.
|Danske Bank Irish Premiership|
|Ballymena Utd||1-0||Dungannon Swifts|