The Rebels remain in fourth place but will know they must take points from the Easter weekend fixtures against Cirencester Town and Chesham United if they are to cement a spot in the top five.
Slough will rue missing first half chances at Latimer Park, with Kettering scoring three times in the second to make sure of the three points.
With five minutes played, Chris Flood played in Liam Enver-Marum, but a combination of James Haran and goalkeeper Paul White prevented him getting a shot away.
Kettering’s Liam Canavan then tested Shaun Rowley from outside the box whilst James Dobson skied a free kick attempt.
The two sides cancelled each other out for most of the first half and created little. Lee Togwell fired wide from outside the box on two occasions, and Gary Mulligan volleyed over from a corner.
Slough had further chances to take the lead with half time approaching, but Nathan Smart poked wide of goal from a Dobson corner, and later Guy Hollis got his head to another corner, but could only send his back post header into the side netting.
And then a minute before the interval, Enver-Marum saw a strike pushed behind for a corner by White.
Slough had certainly edged the first period, but were unable to maintain this in the second.
Rowley saved a scuffed effort from Dominic Langdon on 48 minutes, but could not prevent Kettering from taking the lead four minutes later as James Brighton’s looping header from a long throw found the back of the net.
On the hour mark, Rowley did well to turn a long-range shot from Canavan around the post – but within a minute the same player managed to double Kettering’s lead as he smashed the ball home from the resulting corner.
Rene Howe hit the bar with a header from a corner on 72 minutes with Slough on the back foot, and despite making changes, the Rebels were unable to turn the game around.
Simon Dunn volleyed wide with a quarter of an hour remaining but the Rebels struggled to create openings and Howe sealed Kettering’s win with a third goal in stoppage time, as he curled the ball past Rowley.
Kettering Town Line up
Paul White, Liam Bateman, Jack Kelly, James Haran (Ben Baker), Dominic Langdon, Gary Mulligan, Nathan Hicks, Aaron O'Connor (James Hall), Rene Howe, Liam Canavan (Lewis Hornby), James Brighton. Substitutes not used: Jorrin John, Jack O'Connor.