Florent Hoti missed his penalty after Rochdale goalkeeper Sam Waller stopped it, resulting in Halifax and Rochdale playing to a 0-0 draw at Halifax's home ground.
Tom Pugh earned a penalty kick for the Shaymen in the 82nd minute, but Waller dived the right way to save Hoti's attempt.
The most significant scoring opportunity before the penalty came in the fifth minute when Waller made a fantastic save to deny Zak Emmerson in a one-on-one situation.
Halifax's midfielder Angelo Cappello tried a long-range shot that sailed wide of the goal.
Rochdale came close to scoring in the 65th minute when substitute Devante Rodney nearly assisted Leon Ayinde at the far post.
Halifax, currently in seventh place, are seven points ahead of Rochdale, albeit having played four more matches.