The Shrews extended their unbeaten league run to 14 matches with victory enabling them to take up occupancy of a coveted play-off place.
Rochdale, who accounted for play-off hopefuls Stockport County by a 7-2 margin at the weekend, were no match for an irresistible Shrewsbury side and, although the visitors reached half-time on level terms, the outcome was never in doubt once Leo Fortune-West smashed them ahead in spectacular style just after the break.
Further second-half goals from David Edwards and Stewart Drummond only emphasised the home side's superiority.
As early as the fifth minute the Rochdale goal was under threat and it needed a block from keeper Matthew Gilks and a goalline clearance by defender John Doolan to prevent Shrewsbury grabbing an early lead.
Pressure mounted on the visiting rearguard throughout the first half with the best of a number of chances falling to young midfielder Edwards, who side-footed wide from eight yards after more excellent work from Derek Asamoah.
But after going close to a breakthrough on a number of first-half occasions, there was no denying Shrewsbury their lead just three minutes after half-time.
Fortune-West chased down a long through ball and from 25 yards he crashed a brilliant half-volley beyond Gilks and into the net.
In the 65th minute there was more to admire as a delightful cross from Asamoah was neatly nodded home by Edwards.
The rout was completed when Drummond powered home a header from a Ben Davies corner.