Dan Hicks was handed the captain's armband, and Justin Clayton came into the starting eleven to make his debut. Ryan Hope, Scott Harris and Gürkan Gökmen also started, with Adrian Sear, Lewis Putman and Charlie Mpi dropping to the bench.
Early on, Charlie Strutton sent a header wide as the game flowed from end to end without much goalmouth activity.
Slough took the lead on 24 minutes. Scott Harris beat George Fenton to the ball to meet Sean Fraser's cross and head it past George Legg in the Chesham goal.
Chesham looked to hit back, and Kelvin Bossman was almost played in on goal by Sam Young, but Clayton got a crucial touch to take it away from the striker.
With 39 minutes played, Gürkan Gökmen struck to double Slough's lead. The winger raced onto a long pass and beat Legg to the ball, leaving him the simple task of heading into an open goal inside the six yard box.
Slough took a two goal lead into the second half, and looked to add another with Gökmen firing wide after a neat passage of play involving Hope, Strutton and Scott Harris.
Strutton then burst into the box and saw his shot palmed away by Legg, whilst Adam Martin shot wide on the half volley.
Ten minutes from time, Slough made sure of the win with a third goal. Substitute Putman was played in on goal, and he unselfishly played the ball across to Gökmen, whose shot was blocked - but the ball fell for Strutton, who curled in a low effort.
Legg did well to make a save from Putman's long range free kick, and Paul Stonehouse was also denied by a one-handed save from the Chesham keeper.
Mark Scott was called upon a couple of times to make routine saves, but in truth Slough were rarely troubled and easily claimed a first win over Chesham in any competition in the last 15 meetings, a run stretching back to April 2000.
Chesham United Line up
George Legg, Ashley Smith, Toby Little, Laurie Stewart, George Fenton, Matt Taylor, David Pearce, Sam Young, Kelvin Bossman, Brad Wadkins, Bruce Wilson (c). Subs: George Casey, Stephan Hamilton-Forbes, Ryan Blake, Allen Bossman, Nick Beasen.