McEvilly started his career at Spotland and was re-signed on Thursday from Accrington Stanley, and produced the sort of barnstorming performance that won him international recognition in 2001.
The goal, when it came, saw him round off a neat move with a well-struck left-footed effort from 20 yards in the 67th minute.
Despite their lowly position, Mansfield created the first chance of the game, only for Rory Boulding to see his well-struck drive palmed away by Rochdale keeper Sam Russell.
Slowly but surely the home side took control, but it looked like being an afternoon of frustration, especially when Adam Rundle and then Glenn Murray both missed gilt-edged chances at the start of the second period.
After McEvilly's goal, Dale could and should have extended their winning margin, but failed to make the most of their opportunities and the nearest they came to a second goal was a John Doolan effort that struck the woodwork.