New signing Ben Harris emerged from the substitutes’ bench to head Slough in front in the second half, but a defensive lapse deep into added time led to Ravi Shamsi lofting the ball over goalkeeper Jack Turner and into the net.
A scrappy game was to be expected between these two local rivals on a heavy pitch, and Slough knew they were in for a battle without the injured James Dobson and Matt Lench, with Warren Harris only fit for a place on the bench.
Chances were few and far between in the first half – Jefferson Louis ran clear but could only fire at Jack Turner, and minutes later the Slough stopper easily held another snapshot.
Chris Flood tried his luck from a free kick, but Hafed Al-Droubi was equal to it. A better chance came for Flood on 25 minutes as he took a pass from Brad Wadkins and took it past a defender, but his effort was well blocked.
George Wells was unlucky to see his thunderous shot from edge of the box turned around the post by Al-Droubi as half time approached.
Both sides battled to create chances in the second period, with Manny Williams seeing a free kick attempt blocked and Turner making two saves.
Slough needed to freshen things up, and two substitutions almost had an immediate impact.
Nathan Webb replaced Sean Fraser, and within a minute he fired a long-range effort just past the post.
Then, on 76 minutes the industrious Simon Dunn swung in a free kick and Ben Harris capitalised on hesitant goalkeeping from Al-Droubi, nodding the ball down into an unguarded net.
Ben Harris almost doubled his tally four minutes from time, but his effort was cleared.
Slough had dug in deep with a dogged display and looked set to hold on to their single goal lead, but after a stoppage due to an injury to Brad Wadkins, Chesham launched one final attack with Shamsi running clear down the left. Turner made the decision to come out and meet the striker, allowing him the chance to score from an acute angle.
Chesham United Line up
Hafed Al-Droubi, Munashe Sundire, Jhai Dhillon, Matt Bevans, Kieran Murphy (c), Darren Locke, Ravi Shamsi, Adam Watkins, Jefferson Louis, Joe Iaciofano, Danny Green. Substitutes: Scott McGleish, Shane Bush, Lewis Toomey, Oran Swales, Gerardo Smaldone.