The striker helped set up the first for his side on 55 minutes, seconds after coming on, and then grabbed a goal for himself ten minutes later with a poacher's finish.
It was thanks to a determined effort from the Chester groundstaff that the game had been able to take place following the heavy snowfall the previous day which had decimated much of the evening's fixture list.
Rochdale had had a great chance to go in front ten minutes from the interval when substitute Adam Rundle was teed up ten yards from goal, but he was denied by a brilliant block from James Vaughan when he looked odds-on to score.
The visitors then had two let-offs inside as many minutes. First on 42 minutes a Ritchie Partridge cross-cum-shot cannoned back of the crossbar with keeper Frank Fielding well beaten, and then a minute later Ryan Lowe was in the clear and shot wide with just the keeper to beat.
On 49 minutes Partridge was again involved, this time turning Tom Kennedy inside out before rifling an effort on goal which Fielding did well to touch over.
The deadlock was broken ten minutes into the second half when McEvilly, with his first touch after coming on a sub, helped play in Joe Thompson, who made no mistake with a right-foot finish past John Danby from ten yards out.
McEvilly then header over and Rundle was denied with a fine save by Danby at his near post as the visitors took a stranglehold on the game.
The match was effectively ended as a contest on 65 minutes when McEvilly latched on to a loose ball in the area before poking the ball in off the post.
And the striker nearly polished off a superb substitute display, only to see his side-footed effort cannon back off the crossbar a minute from time.