In a typical start to an opening season game both sides cancelled each other out early on with half-chances falling at either end. James Dobson shot over for the Rebels, while Kofi Lockhart-Adams hit an effort straight at Jake Somerville from distance.
As the half wore on, the away side began to look more confident and just before half-time were close to taking the lead when new signing Reece Yorke headed just past the post against his former club.
In the second half Slough started brightly, and came close when Dyer volleyed straight at goalkeeper James Reading from the edge of the area.
The striker, who scored twice in the club's play-off final against Kettering, wasn’t to be denied though as moments later he raced onto a through ball and calmly lobbed on-rushing keeper Reading with the ball bouncing into an empty net.
After the goal Burnham began to look more dangerous as they pressed for an equaliser. They could have got it when captain Nathan Poulton found himself free at the far post and headed for goal. The former Beaconsfield midfielder was denied by a good low save by Somerville.
As the game wore on both sides had good chances with new signing Darryl Thomas shooting wide from a narrow angle for Slough. Then soon after only a great interception by midfielder George Short denied Burnham what would have been a certain equaliser when they were through on goal.
Minutes after that chance, substitute Scott Harris, who had recently returned from injury, found himself free clear on goal - but the striker dragged his shot wide when well-placed.
In injury time though, the Rebels wrapped up the points when captain Jamie McClurg found himself in the area and delightfully rolled the ball into the path of Jake Parsons. He fired the ball into the empty net to help secure victory on the opening day for Neil Baker and Jon Underwood’s men.
Burnham Line up
Reading, Sackey, Phillips, Hewitt, Munday, Christian, Webb, Poulton(c) Lockhart-Adams, Joseph, Hutchinson. Subs: Ajanlekoko, Butt, McDonnell, Couch, Walker.