Rovers – who last reached the final 101 years ago – were never behind as goals from Kevin Moon, Dougie Hill and Grant Anderson heaped more misery on Terry Butcher’s side, who fell to a fourth consecutive defeat.
Raith, who had not scored in their last five games, went in front through Moon (5) after Joe Cardle’s cross has been deflected into his path.
The lead lasted just eight minutes however, the promising Sam Stanton drawing Hibs level with a fine strike from 22 yards that flew in off the upright.
Rovers refused to be cowed and Ross Callachan’s venemous drive was tipped onto the post by Ben Williams although they suffered a blow when Reece Donaldson had to be stretchered off after an accidental clash of heads.
Undeterred, the visitors continued to press and earned their reward when Hill (45) latched onto Anderson’s flick-on and volleyed home.
But the lead lasted barely a minute as Michael Nelson levelled with a towering header right on the half-time whistle.
Moon brought a decent save out of Williams before Anderson’s cute header (63) left Williams flat-footed to put Rovers ahead for the third time.
Stanton and Nelson threatened for Hibs before Ross Laidlaw flew across his goal to keep out Liam Craig’s stinging free-kick.
Nelson hit the goalframe with a header as the pressure mounted but Paul Hanlon had to hack clear as David Smith looked to settle the tie and the Championship club were to hold out for memorable win.