Ryan Bath’s goal on the stroke of half time proved decisive, and Slough were made to pay for missing a penalty in the second half, with James Dobson’s effort rebounding back off a post.
The result leaves Slough in fourth place, now two points behind third-placed Hitchin with five games left to play.
A strong wind and bumpy pitch combined to make conditions very challenging for both sides, with neither able to play the kind of football they are capable of.
Warren Harris almost beat Frome keeper Kyle Phillips to the ball as early as the third minute, but Phillips was able to punch to safety.
Phillips saved from Dobson, who tried to lob the keeper, and also kept out a low effort from Simon Dunn.
Frome, with the wind against them, struggled to make any inroads into the Slough defence and the visitors looked the more likely to break the deadlock. Slough’s best chance came in the 36th minute as Warren Harris shot wide after a header across from Gavin James.
But against the run of play, Frome took the lead in the final minute of the first half. Ollie Knight showed good footwork before slipping the ball through to Bath, and the striker was able to turn his man and produce a shot from a tight angle which rolled past Shaun Rowley and into the far corner.
Slough introduced Liam Enver-Marum in place of Lee Togwell, who had been cautioned, at half time to add greater attacking threat.
But Frome, now with the advantage of the wind, started the second half better with a good spell of pressure ending with James Fitzgibbon shooting well over the bar, whilst Knight later also put a shot off target.
Dobson tested Phillips with a low free kick and then forced the keeper to punch a dangerous cross clear with Enver-Marum in close attention.
Slough were handed a way back into the game in the 68th minute when Dunn was adjudged to have been fouled by Kris Miller – but Dobson was unsuccessful with his second consecutive spot-kick, hitting the base of the post with Dunn unable to head the rebound goalward.
Ten minutes later Phillips produced a crucial save to stop Harris’ header after a long Guy Hollis throw was launched into the box.
It was to prove another frustrating away day for the Rebels, who continued to probe but almost conceded a second on the break. Bath headed a corner kick wide and with two minutes remaining, Knight and Fitzgibbon combined to produce a shooting chance for Fitzgibbon which Rowley blocked with his legs.
Rowley joined the attack for a last-gasp free kick, but time ran out and Frome had earned a hard-fought victory.
Frome Town Line up
Kyle Phillips, Kris Miller, Chris Gregan, Connor Roberts, Clayton Green, George Miller (c), Ollie Knight, Darren Jeffries, Ryan Bath, Mike Bryant, James Fitzgibbon. Substitutes (all unused): Jake Jackson, Jordan Walker, Ben Cleverley, Jon Davies.