Keith Hill's men will now face Darlington in the play-offs and go into the semi-finals on the back of a 10-game unbeaten run.
Shrewsbury were the stronger team in the first half and took the lead after 33 minutes via Asa Hall's header. Ben Davis' free-kick from the left was glanced past Tommy Lee by the Shrewsbury man, although Dale midfielder Chris Basham may have got the final touch.
Rochdale improved after the break and drew level when Chris Dagnall seized upon a handling error from Scott Bevan in the 54th minute. The Shrewsbury keeper came off his line to collect a high ball and twice allowed it to slip from his grasp, and Dagnall made him pay by dispossessing him and firing into an empty net.
Referee Tony Bates courted controversy when he sent off Dale's Ben Muirhead for a second bookable offence, before realising he had not previously booked the right-winger and it was a case of mistaken identity.
The referee had confused Muirhead with left-winger Joe Thompson who had been shown a yellow card earlier in the game.