Leading by a Dave Hibbert goal at the break, Town fell behind in the second half at 3-2 as Rochdale stormed back into the game, yet when David Hunt tied things up at 3-3 with 90 seconds remaining, it appeared the home side would emerge with a point.
But in the dying seconds substitute Kallum Higginbotham put the visitors ahead for the second and final time, as they dramatically snatched a victory their exciting second-half display just about deserved.
From the outset the match was fast and open and it was a surprise that it took 38 minutes for a breakthrough as both sides had each gone close to taking the lead, but seven minutes before the interval Hibbert struck, sidefooting home after Dale keeper James Spencer was unable to hold a Stewart Drummond header.
But barely a minute into the second half Dale were level, Adam Rundle heading home unmarked at the far post, but Shrewsbury were ahead once more just after the hour mark as Drummond scored with a neat left-footed drive from the edge of the box.
However, as this enthralling contest continued to ebb and flow, Rochdale fought back to level on 80 minutes when Glenn Murray met a cross from skipper Gary Jones and nodded in from six yards.
The visitors finally grabbed the lead in the 85th minute when Jones went from provider to scorer, smashing home an unstoppable 20-yarder that took Dale to the brink of the victory.
There just two minutes left when Shrewsbury were awarded a free-kick on the edge of the box and although the initial effort was cleared, referee Cook ordered a retake and second time around Hunt lashed a low shot beyond Spencer and into the net.
But there was still one time for one more incredible twist, with Dale breaking quickly down the left from where an Adam Le Fondre cross found the head of Higginbotham, whose header settled this breathtaking encounter.