A Connor Goldson header late in the first-half gave the breakthrough before Raith’s Ryan Nolan turned home a James Tavernier cross after the break with a late Scott Arfield strike rounding off the scoring to secure Rangers’ place in the last four of the competition.
From Wednesday’s victory over Hibernian, Michael Beale named one change to his side with John Lundstram coming in from the start in place of Ryan Jack.
Rangers started at Ibrox with Allan McGregor in goal and a back four of James Tavernier, Connor Goldson, Ben Davies and Borna Barisic.
Lundstram was joined in midfield by Nicolas Raskin and Todd Cantwell, while Fashion Jr and Ryan Kent provided support for striker Antonio Colak.
It was Rangers who got the action underway at Ibrox, as the home side looked to carve an opening early on against the Championship outfit.
However, the first sight of goal in this quarter-final tie fell for the visitors as Esmael Goncalves picked up a loose ball in the middle of the pitch and tried a speculative effort from the halfway line but it was wide of the target.
Gers were dominating possession in the early stages with captain James Tavernier denied by a fantastic save from Raith goalkeeper Jamie MacDonald before Connor Goldson had a shot deflected wide from the corner which followed.
In another Rangers attack, Borna Barisic delivered an inviting ball into the box which Fashion Jr was able to head into the path of John Lundstram but his powerful volley was just over the target.
With just a few minutes of the first-half remaining, Gers found the breakthrough with a fantastic set-piece. Borna Barisic whipped a lovely delivery into the box from the corner, with Connor Goldson rising to get a powerful connection on the ball and head beyond Jamie MacDonald.
Into the second-half, Rangers were again looking threatening from set-pieces as another Barisic corner was floated into the box but James Tavernier’s shot was deflected wide by a Raith defender.
Dylan Easton had a shot from inside the box held by Allan McGregor before Rangers burst up the other end of the pitch to double their advantage. There was some fortune for the Light Blues as captain James Tavernier found space in the right-flank to deliver a dangerous ball into the box which Ryan Nolan turned into his own net.
With 25 minutes of the match remaining, Beale made a triple change to his side as Scott Arfield, John Souttar and Ridvan entered the field in place of Fashion Jr, Borna Barisic and Connor Goldson.
For Ridvan, it was his first action since October after recovering from a hamstring injury and he was involved in the action instantly as he drove down the left and cut the ball back to Scott Arfield but his strike was blocked by MacDonald.
Two further changes followed for Gers, with Ianis Hagi and Alfredo Morelos introduced in place of Antonio Colak and Ryan Kent.
Ianis Hagi and Todd Cantwell combined in a forward move with Cantwell touching the ball into the path of Scott Arfield who shot low beyond MacDonald to round off the scoring for the afternoon.
RANGERS: McGregor, Tavernier, Goldson (Souttar, 65), Davies, Barisic (Ridvan, 65), Lundstram, Raskin, Cantwell, Fashion Jr (Arfield, 65), Kent (Hagi, 78), Colak (Morelos, 78).
Subs not used: McLaughlin, Jack, Kamara, Wright.
Raith Rovers: MacDonald, Dick, Nolan, Spencer, Connolly, McBride, Lang, Stanton, Easton, Masson (Young, 81), Goncalves (Ross, 68).
Subs not used: Thomson, Mahady, Young.