Scott Davies pushed Grimes' spot-kick onto the post early in the second half and despite having Alex Marrow dismissed for a second bookable offence with 25 minutes remaining, the visitors dug in for a share of the spoils.
Bobby Grant was close to an early opener for the home side when he met Kevin McIntyre's cross six yards from goal, the striker's attempt to scramble the ball past Davies denied by a last-ditch challenge from Dean Howell.
Ryan Edwards was in the right place to block Tom Barkhuizen's goalbound effort and Rochdale stopper Josh Lillis got lucky when his attempt to punch clear a Jamie McGuire drive went horribly wrong, the rebound only just evading Barkhuizen as the frontman pounced.
The hosts had a golden opportunity to land the first telling blow when they were awarded a penalty minutes into the second half when Marrow brought down Grant. But Davies read Ashley Grimes' spot kick and pushed his effort onto the upright.
Fleetwood's cause was hindered when Marrow was sent off midway through the second half for a second bookable offence but the hosts were unable to break through the Cod Army's stubborn rearguard.