Clyde added to Raith's problems by coasting to a 2-0 victory at the Broadwood Stadium.
The visitors belied their lowly league position with a bright start and both Moussa Ouattara and Herve Ebanda shot wide of the target.
Clyde gradually gained the upper hand and went ahead in the 11th minute from a free-kick situation.
Aaron Conway was fouled 20 yards out and recovered to drive the resulting free-kick past the post. However, the Raith wall had moved too quickly and the referee ordered a re-take. This time Conway sent his kick to the other side of the goal and keeper David Berthelot was well beaten.
Clyde should have increased their lead when Conway set up Ian Harty but he shot over the top when it looked much easier to score.
Raith had a chance to level when Joe McAlpine picked out Ebanda whose finish was steered rather than struck and allowed Bryn Halliwell to make the stop.
The visitors passed up another chance when Hamed Sacko came close with a header from Paul Miller's cross.
Clyde eventually doubled their advantage when Eddie Malone drove a free-kick across the area which John Potter tried to convert. His effort spun high and was going wide of the goal when Scott Wilson somehow turned the header back over the keeper's head.
The second half was flat by comparison except for a shot from Raith's substitute Wesley Daly which rattled the crossbar.
However, Clyde's two-goal interval lead proved decisive.