Slough could have taken the lead in the 12th minute as missed clearances in the Frome defence allowed Scott Harris to get a shot in from around 15 yards, but the ball came back off a post.
Frome's Aaron Rodriguez put a header wide, whilst Kris Miller struck a shot straight at Jake Somerville after a surging run.
Leigh Rumbold went close with a headed effort, and Jake Parsons also saw an effort deflected wide late in the half as the two sides went in to the break level at 0-0.
Aaron Rodriguez was off target with an effort from distance after a mistake in the Rebels' defence on 52 minutes, before Brandon Mundy gave Frome the lead three minutes later. Miller, overlapping on the right, was set free by Lewis Haldane, and his low, hard cross was turned home at the far post by Mundy, who made up a lot of ground to reach the ball.
Minutes later, Harris sent a header just wide from a good position, but he redeemed himself by equalising soon after from a James Dobson cross. Harris superbly looped a header over Darren Chitty as the substitute winger whipped the ball in.
Slough had the better of the closing stages, and Eddie Smith hit the side netting, whilst Dylan Bonella saw a shot held by Jake Somerville in the closing stages, but neither side could find another goal to seal all three points.
Frome Town Line up
Darren Chitty (c), Kris Miller, Mark Cooper, Rhys Baggridge, Jack Vallis, Brandon Mundy, Dylan Bonella, Ricky Hulbert, Lewis Haldane, Ben Thomson, Aaron Rodriguez. Subs: Ben Worlock, Omar Simpson, Cameron Brown.