Grant scored the first goal of Keith Hill's second spell in charge at Spotland, cancelling out Jay O'Shea's opener for the Spireites.
But Dale's hopes of securing a win to mark Hill's first home game since he returned as manager were undone when the striker was dismissed five minutes from time after a late challenge on Sam Togwell.
Chesterfield opened brightly and were inches away from the opening goal when O'Shea was teed up by Marc Richards and sent a 20-yard effort against the crossbar with goalkeeper Josh Lillis beaten.
With the home defence struggling to clear their lines, the Spireites went agonisingly close again when O'Shea's sliced shot from the left narrowly evaded Richards at the back post and when the striker managed to find the target Lillis saved his turn and shot from 20 yards.
The visitors took the lead 10 minutes into the second half, O'Shea side-footing home from the left of the penalty area.
Grant scored a 25-yard curler to level the match before seeing red for a late tackle on Togwell in the centre circle.
There was late drama when Richards appeared to be fouled in the penalty area only for referee Andy Haines to wave away appeals. Rochdale broke upfield and it took a good save from Lee to deny George Donnelly and secure the point.