The Rebels needed to be at their resilient best as the Dorset side had the majority of the play, and grabbed a late winning goal with the match seemingly heading for a draw, to complete a remarkable few days for the club following the 4-0 success at Redditch on Saturday.
Weymouth had the better of the play in a goalless first half, but failed to breach a Slough back four which included Sean Fraser at right back, with Simon Dunn coming back into the side to replace Dan Hicks.
Slough grew into the game after a strong start from the hosts. Mark Scott was called upon in the opening minutes to save a shot from distance, and later Aaron Rodriguez’s shot from the edge of the area was saved by the Slough keeper.
Scott again saved an effort from outside the box, this time from Dan Smith, whilst Slough’s first half-chance saw Harris’ shot deflected wide.
Weymouth continued to heap the pressure on, and Jake Wannell should have done better than scuff his shot horribly from Ben Thomson’s pass, whilst an effort from Smith rolled wide of the far post.
Slough struggled to create openings, with a snapshot from Harris going over the bar on 35 minutes and a chipped effort from the winger dropping wide just before the interval.
Early in the second half, Rodriguez went on a rampaging 40-yard run which ended with him shooting over the bar from the edge of the Slough box.
As the game went on, chances were hard to come by with Weymouth continuing to have more of the ball and Slough working hard to win it back.
On 65 minutes, a corner from Dean Evans caused mayhem in the Slough box, going through a crowd of players before eventually being cleared, and shortly after Weymouth had a huge penalty claim turned down as substitute Chris Shephard appeared to have been upended.
Slough were grateful for another save from Mark Scott on 78 minutes as the keeper rushed out to save with his legs, and three minutes later the Rebels hit Weymouth with a sucker-punch.
Harris, on the edge of the box, hit a low effort through a crowd of bodies from Nathan Webb’s pass, and the ball found its way through and into the back of the net to cue celebrations.
Weymouth were limited to shots from distance as they again tried to break the Rebels down, and the visitors almost scored a second on the counter-attack, but substitute Charlie Mpi was inches away from making contact with Gurkan Gokmen’s cross.
A late corner for the hosts was punched clear by Scott and the final whistle sounded to signal a fifth straight league win for Slough.
Dan Thomas, Mark Cooper, Jake Wannell, Billy Lowes, Stephane Zubar, Calvin Brooks (c), Dean Evans, Charlie Davis, Dan Smith, Ben Thomson, Aaron Rodriguez. Subs: Ashley Wells, Jason Matthews, Sam Jordan, Stewart Yetton, Chris Shephard.