Chesham took the lead after nine minutes as midfielder Steve Wales went on a strong run before lashing a left-footed effort past Jamie Jackson from twelve yards.
Slough were restricted to half-chances as Elliot Buchanan fired over the bar from a free kick, and Hibbert and Edwards failed to test Hayward in the Chesham goal as the ball fell to them from corner kicks.
After being on the back foot for most of the first half, Slough defended well and started to threaten more, with Hayes heading straight at Hayward after Hibbert’s shot had been blocked.
Hibbert was then guilty of losing possession 30 yards out, but Steve Wales’ fierce low shot was dealt with by Jackson.
Slough had the first chance of the second half as Hayward fumbled a long floated free kick. The ball fell to the feet of Bowden-Haase, but his effort was cleared off the line.
Chesham scored a second goal as Leon Archer’s pace allowed him to get in behind the Slough defence, round Jackson and slot home confidently.
Hayward had to be alert to deny Danny Murphy, a first-half substitute for the injured Chris Herron, from a well-struck free kick, the keeper parrying the initial shot and the kicking the ball away with Martin and Edwards lurking.
Slough did manage to pull a goal back on 68 minutes. Simon Martin controlled the ball beautifully as the ball was knocked down from a long throw, before firing high into the net from a tight angle.
The Rebels were however unable to find the equaliser as Chesham stood firm, and were almost caught out a third time late on. A promising move broke down, and Chesham counter-attacked through Archer, but substitute Burnell was denied by a crucial block.
Chesham United Line up
Hayward, Kyriacou, Bardle, Adedeji (c), Laws, Lambert, Fotheringham, Wales, Archer, Bangura, Marsala. Subs: Parker, Burnell, Pattison, Ledger, Talbot.