The Rebels went into the game without both Guy Hollis and Eddie Smith, both of whom were unable to make the trip, leaving striker Scott Harris to fill in at centre back.
Frome went close as Marcus Mapstone headed over a free kick from George Miller, and despite Slough showing their own attacking intent with Lee Barney proving a handful, the home side took the lead on 19 minutes.
Dan Hicks fouled Mitchell Page, and after Miller had seen an initial shot blocked, the ball rebounded to Steve Hulbert, who found the bottom corner from just inside the box.
Minutes later, Mark Scott saved with his legs from James Fitzgibbon as Frome spurned a good chance to double their lead, and instead Slough equalised. Lewis Putman stepped up to shoot from a free kick 25 yards out, and the ball deflected off the wall and up over Darren Chitty's head into the opposite corner of the goal.
Slough had the better ball possession and territory with Barney being denied by a great tackle from Sam Teale, and the striker was thwarted again by Chitty shortly before the interval. Gurkan Gokmen produced a fine point blank save from the Frome keeper also.
Chitty was kept busy early in the second half, first making a fine reaction save from Warren Harris before gathering another effort from the winger more easily.
Barney was then played in on goal and he forced another good save from Chitty as Slough kept the pressure on.
But against the run of play, Frome regained the lead with an unusual goal. Teale played a free kick into the box from just inside the Slough half, and Scott misjudged the flight of the ball as it was caught in strong wind, seeing it fly into the back off the net.
Frome defended resolutely for the remainder of the game as Slough struggled to create another clear cut chance. Jake Parsons shot wide from distance and Putman sliced an angled shot wide.
The hosts almost snatched a late third goal when Dan Hicks, under pressure from Jake Jackson, tried to play the ball back to Scott only to almost concede an own goal, but Scott Harris, who had a fine game despite being played out of position, got back to rescue the situation.
Frome did well to slow the game and run the clock down as time ran out for Slough to find the equaliser which was the least they deserved.
Frome Town Lineup
Darren Chitty, Jordan Walker, Sam Teale (c), Rob Hobbs, Steve Hulbert, Marcus Mapstone, Jon Davies, Darren Jefferies, Mitchell Page, Dan Cleverley, James Fitzgibbon. Subs: Chris McPhee, George Miller, Jake Jackson, Jordy Nkunga, Kris Miller.