In what had been an evenly-matched contest, Shrewsbury took the lead through former Dale favourite Grant Holt but were unable to hang on as McEvilly and fellow substitute Chris Dagnall turned the game in their side's favour.
An even first half saw few chances with perhaps the best falling to home winger Joe Thompson but he saw his low angled drive brilliantly cleared off the line by defender Kelvin Langmead.
The visitors took the lead when their leading scorer Holt, a cult figure during his time at Spotland, produced a fantastic turn and even better left-footed finish to score his side's first goal in over 360 minutes of football.
Undaunted, the home side simply racked up the pressure and drew level some seven minutes later.
They might have had a penalty but referee Foster awarded them a free-kick literally on the edge of the penalty area and McEvilly stepped up to calmly curl it around the wall and beyond the despairing dive of the poorly positioned Luke Daniels.
The home side weren't content with a share of the points and continued to press and they were rewarded with just seven minutes to go when Dagnall's header from a Clark Keltie corner was hooked off the line by Darren Moss but bundled home from close range by McEvilly as he registered his first brace of a third spell at a club that he calls "home".
Dale certainly didn't sit back on their lead in the late stages and only a terrific save by keeper Daniels denied Adam Rundle a fine individual goal and from the rebound Ciaran Toner blazed over.
The victory sees Rochdale leapfrog Shrewsbury as they move back into the play-off places but at the same time moves the big-spending Shrews out of the top seven.