The Rebels named a squad of 16 for the match, with five players playing a full 90 minutes in difficult conditions.
Slough missed clear opportunities through Guy Hollis and Matt Lench, whose 20-yard effort swerved over the crossbar, before Wealdstone took the lead just before half time, with Josh Umerah slotting past Jonathan North from six yards.
In the second half, Alfonso Tenconi - a surprise inclusion before his departure for Stanford University - headed a leveller from a fantastic James Dobson cross on 56 minutes.
Twenty minutes later, a Wealdstone trialist hit the crossbar from 20 yards, with the ball bouncing off North’s back before being cleared.
Late on, Wealdstone regained the lead through a trialist and went on to win the match.
Slough are back in action at Arbour Park on Tuesday evening, welcoming Winchester City.
Slough Town Line up
Jonathan North, Joe Dandy, George Wells, Guy Hollis, Edon Pruti, Matthew Lench, Elliot Benyon, Johnny Goddard, Scott Davies, Fabio Sole, Aaron Kuhl. Substitutes (all used): Josh Jackman, James Dobson, Alfonso Tenconi, Manny Williams, Imran Kayani.