In the first half, Burnell fired a warning shot wide and Ashford had a goal ruled out for offside as both sides came to grips with playing football again after the enforced break.
Slough took the lead on 31 minutes when Ashford keeper Jack Franks allowed a tame effort from Steve Sinclair from the edge of the box to evade his grasp and end up in the back of his net.
Just eight minutes later, Sinclair doubled his and Slough’s tally as he picked up a half-cleared corner on the end of the box and half-volleyed a superb effort past Franks, who this time stood little chance.
Franks did well to deny Slough a third before the break as he tipped Simon Martin’s crashing long-range effort onto the post and behind.
With Paul Coyne dominating the midfield and Simon Martin holding the ball up well, Slough looked a constant threat, and Martin himself was denied a goal as he received the ball from Burnell and struck a left-foot shot towards the near post, which Franks turned behind.
Another attempted lob from Sinclair dropped just wide as Slough continued to press, and Ben Abbey hit the bar with an attempted cross - but Ashford had their chances as Kansk dragged a shot wide.
Despite looking in control for much of the second half, a goal from Tyrone Berry with ten minutes remaining ensured a nervy finish, but the Rebels held on to record their fourth straight league victory.
Ashford Town (Middx) Line up
1. Jack Franks, 2. Samad Kazi, 3. Aknasi Edusei, 4. Russell Canderton, 5. Billy Jeffreys (c), 6. Alain Behi, 7. Tyrone Berry, 8. Luke Hickie, 9. Jones Awuah, 10. Jamie Lawrence, 11. Thomas Kansk. Subs: 12. Harry Franks, 14, Mark Bitmead, 15. Martynas Butkus, 16. Oscar Luizwama