An early goal from skipper Sam Teale set the Somerset side on their way, as he volleyed in from Jon Davies' free kick delivery in the fourth minute.
Once again, Slough had conceded the first goal and found themselves chasing the game. Frome continued their positive start though, and George Miller's 20-yarder was easily saved by Mark Scott, and a minute later, Mikey Bryant almost doubled the lead, but Scott blocked with his legs.
In response, Slough's first effort at goal came from Lewis Putman on 16 minutes, as he came inside from the right and fired wide after one-touch build-up involving Simon Dunn and Charlie Moone.
Frome danger man Davies put a shot wide after a strong run, and Nathan Smart's last-ditch headed clearance denied the visitors a second goal from Kris Miller's deep cross.
The visitors were much the better side for large spells and Slough barely laid a glove on them in the first half, with Frome seemingly first to every ball and putting the home side under pressure every time they had the ball, forcing the Rebels into aimless long balls forward.
Half time arrived with no further clear chances for either side, and Slough started the second half more positively but did not trouble Frome keeper Kyle Phillips.
Davies was stopped by a superb last-ditch tackle from Sean Fraser on the edge of the box as Frome broke clear after an apparent foul on substitute Nathan Webb was missed.
Charlie Moone headed Slough's best chance over from three yards on 59 minutes, though it was far from easy as he tried to divert James Dobson's driven cross on target.
Slough's general play remained rushed and ineffective due to the pressure Frome put on the Rebels when in possession, and attempts at goal became more and more desperate - Dobson's 35-yard attempt, which flew well wide, a good example.
And on 67 minutes Ollie Knight steered the ball home from 10 yards after a cross from the right to give Frome the cushion they deserved.
A matter of minutes later, Slough were handed a lifeline as a penalty was awarded for a foul on Moone. Dobson lashed the spot kick home despite Phillips getting a good hand to the ball.
This looked to have set up an interesting last twenty minutes, but Frome stopped a disappointing Slough from mustering another chance and held on comfortably, handing the Rebels a fourth league defeat of the season.
Frome Town Line up
Kyle Phillips, Kris Miller, Sam Teale (c), Connor Roberts, Marcus Mapstone, Clayton Green, Jon Davies, George Miller, Jake Jackson, Mikey Bryant, Ollie Knight. Subs: Chris Cragan, Nathan Summers, Aidan Kirby, Dean Griffiths, Ben Cleverley.