Sam Stanton, Matej Poplatnik and Aidan Connolly were on target in a match that the Kirkcaldy side dominated from start to finish.
Raith made two changes from the loss to Arbroath last week; Dario Zanatta and Tom Lang started with Kyle Benedictus and Reghan Tumilty dropping out for a match which John McGlynn’s side totally dominated.
It was one-way traffic for almost the entire match, most in the 870 in disbelief that Raith failed to score in the first 45, passing up a number of good chances with the hosts unable to get out of their own half.
Jamie Gullan had the first attempt after just a minute had been played but the striker mishit his shot.
He went close again with a low drive just moments later which was well turned aside by ‘keeper Fraser Hobday.
From the resultant corner a shot from Raith captain Christophe Berra was blocked on the line.
On 13 minutes a chip from Berra found Ross Mathews in space but Hobday was sharp off his line and did well to block the midfielder’s attempt.
Gullan tried again with a shot on the turn which went wide before narrowly failing to connect with a cross from Dario Zanatta on 19 minutes.
Frankie Musonda went close with a terrific drive at goal but it was just too high on 23 minutes, as was a header from Ethan Ross 10 minutes later.
A shot from Berra went well wide and both Liam Dick and Tom Lang went close with headers.
Somehow, the sides went in at the break with the score still 0-0.
The second half began in the same fashion with Raith having the vast majority of possession and Hobday pulling off a superb save from a Berra close range header.
Musonda hit the post with a header on 57 minutes as the Aberdeen side held firm at the back, but, just as doubts as to whether Raith would ever score began to creep in, they finally made the breakthrough.
A free kick from sub Connolly on 65 minutes was deflected into the path of Stanton just six yards from goal and he made no mistake.
An effort from Musonda was high before Ben Williamson flashed a shot wide.
The home side finally had an effort on goal with nine minutes remaining; Jamie MacDonald, a virtual spectator by this point, doing well to push away a free kick from Lachie MacLeod after the same player had been fouled by Lang.
With just a minute to go Raith made sure of the win - sub Poplatnik scoring with his very first touch of the ball, turning in the loose ball after Hobday had parried a shot from Ross.
In injury time a header from Berra almost crept in before Raith made the scoreline more reflective of their overall play.
Poplatnik fed Connolly as they hit Dee on the break and he curled the ball in off the post to make the final score 3-0 and send Rovers into the draw for the fifth round.