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McEveley drove in an unstoppable shot two minutes from the end of normal time to end a run of three consecutive defeats against the South Yorkshire club.
The result was tough on Doncaster who could not make their possession count and repeat December's Championship victory at Derby.
They had shown what a dangerous side they are on the counter-attack at Pride Park in December and they had the better of an open first half.
John Oster wasted a great chance to shoot when Derby's defence melted in front of him as he ran into the box, but his attempted pass was the wrong option and Billy Sharp failed to find the power to trouble Stephen Bywater from the edge of the area.
Derby had faded after a purposeful start, but they created a good opening in the 44th minute when Steve Davies put Stephen Pearson in, but Neil Sullivan was off his line quickly to save at the midfielder's feet.
Rovers continued to look the brighter more inventive side in the second half although it was a mistake by Robbie Savage that allowed Sharp to get in a shot that was charged down and Mark Wilson's follow-up forced Bywater into a diving save to his right.
Derby responded with a good move down the right in the 55th minute that ended with Nicky Hunt crossing and Davies headed just over the bar.
A miskick by Hunt let in Gareth Roberts to deliver a low cross that Sharp just failed to turn in at the back post, but Derby had another good chance when Davies was given space on the edge of the area but he shot wide.
Derby were close to going ahead eight minutes from the end when Pearson crossed low, but Kris Commons was denied by a crucial block from Sam Hird and Sullivan then saved Pearson's drive.
Sharp almost got his head to a James Coppinger cross, but McEveley won it for Derby when he pounced on a rebound to fire a 25-yard drive into the top left corner.