The Shots began brightly Jayden Harris fired straight at Jonathan North after being played through on goal following a neat passage of football.
Slough responded with Freddie Grant heading over the bar from a corner.
Later, Max Worsfold made progress down the left side before firing wide of Mitch Walker’s goal.
Toby Edser came closest to opening the scoring in the 28th minute with a stinging drive from 25 yards, but North was equal to it with a brilliant save.
Minutes before the break, Josh Jackman was denied a spectacular goal when Walker tipped his fiercely-struck volley over the bar.
Early in the second half the Rebels went close again when Eitel Goueth struck an effort narrowly off target.
But on the hour mark, Aldershot struck twice in three minutes, both goals coming from Trialist A. First, he put the visitors ahead from just inside the penalty area, rifling in with his left foot after good work on the right by Trialist C.
Then less than two minutes later he was on hand to slot home another at the second attempt, ably assisted by Corie Andrews.
Slough pulled one back on 75 minutes, with Aaron Kuhl converting from the penalty spot after a trip on Paul Hodges in the box.
North needed to make one final stop in the last minute as he deflected behind a strike from Watts, who created the chance for himself.
Slough Town Line up
Jonathan North, Josh Jackman, Freddie Grant, Mark Nisbet, Max Worsfold, Matt Lench, Ben Harris, Eitel Goueth, George Hunt, Ryan Bird, Joe Lawal. Substitutes: Tom Derry, Scott Davies, Aaron Kuhl, Sean Fraser, Gabe George, Paul Hodges.