Anthony Stokes put Hibs ahead with his third goal in two games.
But Lewis Toshney and Mark Stewart scored either side of half-time for the hosts.
Alan Stubbs' side have two games in hand over Falkirk, but have now lost four consecutive league games, while Raith sit seven points clear in fourth.
After scoring both in a midweek Scottish Cup quarter-final triumph in Inverness, Stokes fired a half-volley low beyond Kevin Cuthbert to open the scoring.
Soon after, though, Hibs captain David Gray and Darren McGregor failed to deal with a long ball from Craig Barr. It was an innocuous enough punt downfield, but the duo allowed the ball to ricochet between them, Toshney stealing in to score.
With the second half underway, Liam Fontaine diverted Ryan Hardie's low cross on to his own post, and from the resulting corner Stewart nodded home.
Jason Cummings has not scored since 16 February and the striker produced a contender for miss of the season when he struck the underside of the crossbar with an open goal to hit from a yard out.
The youngster was withdrawn for Farid El Alagui and sat with his head in his hands on the bench.
Ryan Hardie prodded wide from six yards as the hosts pressed for a third.
And substitute Chris Dagnall, a January signing who has yet to score for Hibs, curled a close-range effort just wide in the final 10 minutes, before his late looping header came back off Cuthbert's right upright.
Hibernian remain six points adrift of second-place Falkirk in the Championship after falling to defeat at Raith Rovers.