The Championship side had failed to score in their previous five matches but Kevin Moon, Dougie Hill and Grant Anderson were all on target for Rovers, who were twice pegged back by equalising strikes from Sam Stanton and Michael Nelson.
It was another miserable afternoon for the hosts - beaten finalists in the last two years in this competition - and Terry Butcher's side were booed off at the final whistle.
Hibs made a bright start and Rovers goalkeeper Ross Laidlaw was called upon inside two minutes to prevent his side from going behind.
Alex Harris' corner eventually made its way to Liam Craig and his deflected shot was flicked goalwards by James Collins - but Laidlaw got down well to his right to push the ball behind for another corner.
Raith survived and then stunned their visitors by taking the lead after five minutes through Moon.
Joe Cardle skipped past Nelson on the flank and his low cross was diverted towards Moon by Hibs defender Paul Hanlon. The midfielder slid a low first-time left-footed strike beyond Ben Williams from 12 yards.
Hibs were level in the 14th minute with a fine drive from Stanton. The talented youngster's first touch took him inside from a Tom Taiwo header and he drilled a low left-footed drive beyond Laidlaw in off the post.
On a threadbare pitch, Hibs struggled to build on the momentum of their equalising goal, while at the other end Raith forward Ross Callachan thundered a low drive from 25 yards back off Williams' upright after Greig Spence pressured Hanlon into making a mistake.
Raith were forced into a change before the half was out when Reece Donaldson was taken off on a stretcher in the 43rd minute with a head knock after being caught inside the box by Craig.
However, the visitors put that setback behind them to storm back in front a minute later. Substitute Fraser Mullen's free-kick was flicked on by Anderson and Hill cushioned a volley past Williams from close range.
There was time for more drama before the interval, however, as Hibs equalised in first-half injury-time after Craig's corner was headed in by Nelson at the back post.
Hibs created the first chance of the second half but Stanton's fierce effort from distance just missed the target.
Raith responded with a chance of their own but Moon drilled a close range shot straight at Williams after being teed up by Anderson.
Callachan tried his luck from distance in the 57th minute but a low right-footed drive bounced harmlessly wide of the post.
Rovers then went ahead for the third time in the 62nd minute with a clever header from Anderson. Cardle did well to work space for a cross from the left flank and his teasing delivery was diverted high into the net by Anderson.
Raith goalkeeper Laidlaw kept his side's slender lead intact ten minutes from time when he repelled a fierce Craig free-kick from 20 yards. From the resulting corner, a looping Nelson header hit the bar from Craig's delivery.
Hibs substitute Paul Heffernan then wasted a good chance with minutes left when his tame shot was well held by Laidlaw after being set clear by Craig.
Fellow Hibs replacement Danny Haynes then had a near-post effort cut out by Laidlaw as the hosts pressed - without success.