League One player of the month John Marquis, however, just could not add to his eight goals for the campaign, missing a hat-trick of chances as James Wallace and Ashley Eastham made it 3-0 to the visitors before the break.
Ashley Hunter made it 4-0 in the 49th minute and there was no way back for the hosts as Fleetwood recorded their first win at the Keepmoat.
Rovers had seen a seven-match unbeaten League One run end in a 1-0 defeat at Accrington Stanley in midweek but manager of the month Grant McCann named an unchanged side.
His starting line-up included former Fleetwood duo Danny Andrew and Matty Blair, while Doncaster-born Alex Cairns was in goal for the visitors
Evans led the Fleetwood attack after replacing Wes Burns from the side which drew with Wycombe in midweek.
Evans struck in the fourth minute when he chased a long ball down the right, took a touch and was brought down inches inside the area by Marko Marosi, who had dashed out to his left. Evans struck home the resulting penalty although Marosi got a glove to the ball diving to his right.
Doncaster struck back and former Rovers defender James Husband was booked for putting an arm across Mallik Wilks as the striker attempted to reach a through ball. The Fleetwood left-back also went down clutching his hamstring and had to be replaced before Herbie Kane bent the 22-yard free-kick over the bar.
Holt went into central midfield and Ryan Taylor to right-back from where Leeds loanee Lewie Coyle came over into Husband's position.
With Coyle out of position following a raid down the flank, Wilks cut in from the right, turning Eastham before firing a fierce shot which Cairns beat away.
Marquis should have equalised but headed wide from a chip from Wilks in the 29th minute and Joe Wright also headed off target following Rovers' first corner.
Fleetwood forced their first corner and Ashley Hunter's flag kick was met by the head of James Wallace, giving the visitors a 2-0 lead from six yards in the 34th minute.
Marquis was again out of the luck going down the middle but failing to beat Cairns, who had rushed out 16 yards, with an attempted chip.
Joe Wright, James Wallace and Evans all went in the book as tempers frayed.
Marquis fired over from eight yards in stoppage time and it got worse for Rovers as central defender and Fleetwood captain Eastham headed home from eight yards from Ross Wallace's corner.
Fleetwood club captain Craig Morgan, on his way back from injury, replaced James Wallace at the break, moving into central defence with Nathan Sheron going to right-back.
it was soon 4-0 as Wright was robbed in possession by Hunter, who raced on and planted the ball past Marosi before celebrating with a somersault.
Marquis had another shot blocked after being teed up by substitute Ali Crawford.
Alfie May and Alfie Beestin also came off the bench to no avail, Rovers captain Andy Butler having to depart with a left collar bone injury which left them a man short in the closing stages.