A squad containing mainly trialists and Academy graduates Kyle Brooks, Oscar Lucey, Eitel Goueth and Kai Allsopp - as well as the much more experienced Gabe George, made captain for this game - made the short trip to Burnham.
Also in the squad was Louis Walsh, who featured last season, and Leon Chambers-Parillion, whose previous spell at the club on loan from Oxford United was cut short through injury.
Combined Counties Premier Division North side Burnham took an early lead, before Goueth levelled with a curling effort into the top corner.
George Butler gave the home side the lead again on 17 minutes, but Slough equalised with Walsh sliding the ball past Carl Dennison.
Slough took a 3-2 lead into the break, with Allsopp firing into an empty net after Dennison had pushed away a cross from the right side.
There were chances for both sides, but Burnham levelled in the second half and found a winning goal late in the game.
Next up for the Rebels is a trip to Ascot United on Tuesday evening (7.45pm).
Slough Town Line up
1. Kye Plumley 2. Kyle Brooks 3. Tyrese Dyse 4. Blaise Riley-Snow 5. Gabe George 6. Oscar Lucey 7. Louis Walsh 8. Eitel Goueth 9. Temi Akinbusoye 10. Kai Allsopp 11. Leon Chambers-Parillion 12. Joel Nakatani-Brown 13. Nick Inwugwu 14. Ben Ssengo 15. Will Dupray 16. Josh Andrew 17. Harvey Harry 18. Gedeon Okito 19. Hamza Semakula 20. Darnell Baxter-Alleyne