Hayes started the game brightly and went ahead on 12 minutes as Lawrie Shennan buried a cross-shot at the back post.
Slough keeper James Warrington then kept it at one with a good save before Hayes hit the post. But Slough levelled on 26 minutes as Ed Smith's attempted cross flew past Ben Goode at his near post.
After a break in play due to an injury to Warrington, the Rebels went ahead on 39 minutes after a spell of pressure. Dan Burnell did superbly to keep the ball in play and Dave Deeney worked the ball to Burgess, who fired past Goode to punish some static Hayes defending.
Slough started the second half well but missed chances to extend their lead, Parsons seeing a shot saved and Smith also going close. But Warrington also had to be at his best to turn away a strike from Tash Jordan as the visitors broke away.
Hayes pushed forward and threatened an equaliser in the closing stages but Slough were able to close the game out and seal the points.
AFC Hayes Lineup
Ben Goode, James Walters, Charlie Crane, Ben Dyett, Tom Martin (c), Ben Butler (Andrew Harewood), Tash Jordan, Mitch Gough, Lawrie Shennan, Tony Mendy (Adam Willis), Aban Majeed (Lawrie Walters). Subs not used: Sean Mangan, Michael Vincent.