The home side went on the attack early on, winning three consecutive corners – the third of which resulted in a foul on goalkeeper Kyle Phillips.
It was a good start, but the Rebels were caught out on 11 minutes as Frome took the lead. They attacked down the right and talisman Jon Davies whipped in an inch-perfect cross which captain George Miller headed beyond Jack Turner.
Frome then let Slough off the hook three minutes later as Joe Raynes fired wide after hard work from Mitchell Page to create the chance, beating Guy Hollis to the ball before squaring it.
Slough responded with Lee Togwell crossing in for Manny Williams, who volleyed over. Williams was again in the right place on 20 minutes as he got on the end of a cross from George Wells, but could only head it straight at Phillips.
Slough had plenty of the ball but were left frustrated as a well-organised Frome kept them out for the remainder of the half.
But the second half was a different story, and three minutes into the second period, Slough were level. James Dobson – who switched to play on the right side to offer a different attacking threat – swung in a corner, and Chris Flood got in front of the otherwise impressive Phillips to glance a header into the net.
The Rebels went on to dominate, and Frome had Phillips to thank three minutes later as he denied Williams following a through pass from Flood.
Philips kept out another low strike from Williams, and a fearsome strike from Hollis was also well held by the keeper.
Slough deservedly went ahead on 66 minutes as Simon Dunn seized upon a cross from Wells which Frome had failed to clear, and he brought the ball onto his left foot before firing it into the bottom corner.
Phillips then made a crucial save to prevent a certain own goal from Connor Roberts as Frome started to look uncertain at the back.
Frome provided Slough with a few nervy moments in the final five minutes, as first Chas Hemmings was denied by a goalmouth block, and then Davies slammed into the side netting.
Dobson was gifted possession soon after and tried to lob Phillips, but the ball dropped wide – and moments later Frome substitute Ryan Bath appeared to be fouled in the box, but his claims were waved away.
Slough broke away one final time and Phillips produced a super low save to turn Matt Lench’s strike around the post as the Rebels saw out the win, their first in nine games against the Somerset side.
Frome Town Line up
Kyle Phillips, Kris Miller, Ben Withey, Connor Roberts, Marcus Mapstone, Chas Hemmings, Jon Davies, George Miller (c), Mitchell Page, Joe Raynes, Darren Jefferies. Substitutes: Ollie Knight, Sam Teale, Ollie Knowls, Ryan Bath, Ben Griffiths.