Chris Brown marked his home debut with an early penalty and set up the second for Ryan Mason.
And the on-loan Tottenham playmaker in turn became the provider for another summer signing, Kyle Bennett, to superbly round off the win.
The home side were ahead inside five minutes after John Welsh fouled James Coppinger in the box and, after a long wait, Brown tucked away the spot-kick.
Coppinger tested Tranmere keeper Owain Fon Williams but the visitors went close to an equaliser shortly afterwards when Andy Robinson's corner was met by defender Ian Goodison, Richard Naylor blocking the Jamaican's effort.
Both teams then threatened from corners, with Brown's effort saved by Fon Williams before Mark McChrystal fired over at the other end.
Brown was again involved as Doncaster doubled their lead shortly before the half-hour mark as he teed up Mason to find the net from 12 yards out.
They went close to a third when Mason was denied at close quarters by Fon Williams from Sam Hird's cross and Bennett fired the rebound over from inside the six-yard box.
The irrepressible Mason drew a fine diving save from Fon Williams but Adam McGurk gave encouragement to Tranmere when his effort was saved by Gary Woods.
Mason then laid the ball back for Bennett to announce himself to the Keepmoat Stadium faithful with a wonderful third, chipping Fon Williams from 25 yards.
Substitute Giles Barnes, signed on a six-month deal after his release by West Brom, twice went close to a fourth and Zoumana Bakayogo blocked Coppinger's drive.
But three goals proved more than enough, with John Oster's lob drifting over from the last effort of the game.