The full-back benefited from Robbie Savage dispossessing John Oster and rifled a left-foot shot into the far top corner from the edge of the box.
It was harsh on Doncaster who had beaten the Rams in each of the three league meetings between the sides since their promotion to the Championship in 2008, including a 2-0 win at Pride Park last month.
With in-form striker DJ Campbell ineligible under the terms of his loan spell from Leicester, Chris Porter returned to the Derby starting line-up. Rovers were unchanged from their midweek cup win at Brentford.
Doncaster went close early on when Billy Sharp headed James Coppinger's cross wide.
Steve Davies sent a shot from the edge of the area wide after 18 minutes as Derby threatened for the first time.
Sharp warmed Stephen Bywater's palms with a well-struck effort from 25 yards midway through the first half.
The Rams responded when Nicky Hunt flashed a shot narrowly wide from the right side just before the break.
Sharp shot straight at Bywater from long range and Davies shot wide as the second half began in a familiar vein.
Brian Stock sent a low shot through a crowded penalty area just after the hour mark but his effort also missed the target.
At the other end, Neil Sullivan made a routine save to deny Kris Commons but there was nothing the veteran keeper could do about McEveley's piledriver two minutes from time.
Bywater saved from Lewis Guy in the third of four minutes of injury time but the shot was never going to trouble the keeper.