Raith keeper David Berthelot was involved in early goalmouth action to finger-tip away an effort from Craig Bryson, whilst at the other end a Paul McMullan cross was easily gathered by Bryn Halliwell.
Clyde's best player, Mark Gilhaney, was giving the Raith defence a hard afternoon, and he caught them napping once or twice with the long ball out of defence.
The first time he cut in to give himself a better angle for his shot, but delayed too long and eventually wasted the opportunity by having a shot when a square ball to his colleague might have produced a goal.
The second time, however, he gathered Eddie Malone's pass to run on into the area and beat the advancing Berthelot with a low shot.
Clyde's main striker this season, Ian Harty, was having a complete off day and scorned several chances to put the game well beyond the visitors. His main supply came from Bryson, but even when one-on-one with Berthelot he shot weakly from close range and allowed the Raith keeper to turn the ball away for a fruitless corner.
Clyde eventually produced a move worthy of note involving Gilhaney, Bryson and Alex Burns, but the latter spoiled a great build-up by shooting over the top.
This narrow victory was Clyde's first in the last six games.