Both sides had shots blocked around the edge of the box early on, with Eddie Smith crowded out after good play by Gurkan Gokmen to create the chance.
At the other end, Lewis Haldane went close after Frome broke away from a Slough corner, but the striker’s effort was blocked as he looked to poke the ball past Luke Williams.
Frome committed men forwards in search of a goal, but could not find a way through and the visitors fell behind on 36 minutes.
The goal owed much to the hard work of Dan Read out on the right, but also to some poor defending as Frome failed to clear his cross away, leaving Chris Henry able to bundle the ball home from close range.
Gokmen headed over a Sean Fraser cross minutes later, and defender Rhys Baggridge put a free header wide of Williams’ goal from a free kick.
Smith then thought he had doubled Slough’s lead as he lobbed the ball into the back of the net, but was denied by an offside flag.
Slough held a slender half-time lead, and looked to double it early in the second half, with Smith turning superbly past his man, but sending his attempted shot well off target.
Frome grew in confidence, and Williams did well to hold a fierce strike from out wide, before Chris McGrath got himself in a good position, but his cross-shot missed everyone in the middle.
The visitors had a good spell of pressure around the Slough box without seriously troubling Williams, and Smith again could have found the back of the net, but this time was denied by a top save from Darren Chitty, the keeper turning behind an overhead kick from the striker.
However, the Rebels were made to pay for a lapse in concentration on 71 minutes. A free kick was delivered in from the right by Matt Smith, and defender Jack Vallis rose above the Slough defence to head past Williams, who was beaten to the ball.
Frome continued to push men forward, but were almost caught out as Smith controlled the ball well and fizzed a shot goalwards, but Chitty was on hand to claim the ball.
Smith continued to be frustrated by Chitty as another effort was turned away by the keeper.
Late on, Frome went close to snatching all three points, with substitute Ben Thomas shooting straight at Williams after being teed up by Ricky Hulbert – and with the last chance of the game, Hulbert went very close with a shot from distance, but the ball flew past Williams’ post and his side had to be content with a point on the road.
Frome Town Line up
Darren Chitty (c), Mark Cooper, Anthony Tomkin, Rhys Baggridge (Ben Thomson), Jack Vallis, Chris McGrath, Ben Worlock, Matt Smith, Lewis Haldane (Kris Miller), Ollie Taylor (Matt Cowler), Ricky Hulbert. Sub not used: Matt Minnis.