Shrewsbury took the lead on six minutes when Luke Rodgers tumbled theatrically to the ground following a challenge from Greg Heald, and veteran Mike Sheron calmly converted from the spot.
Following constant home pressure Rickie Lambert drew his side level with a 30-yard rocket just before the break and the former Stockport midfielder, playing out of position as a striker, went close on several other second half occasions as his side camped in the Shrewsbury half.
Just after the break Lambert shaved the crossbar with a left-footed drive and then saw keeper Joe Hart somehow keep out his stinging right-footed volley.
Marc Richards, courtesy of a Lambert header, saw his effort somehow kept at bay by the feet of Hart, and following a flowing move, again involving Lambert, Kiwi winger Leo Bertos saw his effort shave the post.
At the other end Shrewsbury's only other effort of note saw Rochdale keeper Matthew Gilks produce an excellent save to deny Rogers after the livewire striker had got on the wrong side of defender Gareth Griffiths.