The Rebels came out the blocks fast and in only the 6th minute, they opened the scoring.
Johnny Goddard danced past the defence, before striking his effort against the base of the post and into the back of the net.
On 36, Slough doubled their advantage thanks to a well-orchestrated team move in the final third of the field.
Aaron Kuhl whipped a delightful ball into the box which Elliot Benyon headed back across goal for Matt Lench to confidently fire the ball into the net from close range.
Moments later, the deficit was halved thanks to Brandon Adams, whose sharp strike from inside the area found the bottom corner, leaving Slough stopper Jonathan North with no chance.
The hosts extended the lead back to two goals midway through the second half, thanks to a fine strike from red-hot Goddard.
The winger cut inside from the edge of the box to delightfully curl his strike beyond the scrambling Cheshunt keeper, he was running riot throughout.
The action got nasty as the visitors’ defender Raul Da Silva was issued two yellow cards for a foul, followed by a display of petulant behaviour right after.
Slough didn’t have it all their own way, particularly in the first half as North had to react quickly to palm Dayshone Golding’s rasping drive over the bar from close range.
Cheshunt were bringing some physicality to the game, but Slough managed to play through the press and Ben Harris fired into the side-netting from close range when he will feel aggrieved not to hit the target.
Scott Davies also saw his freekick curl wide of the post in the second half, and Elliot Benyon had chances, one of which being a diving header which looped over the bar.
It was a well-deserved three points on home soil, with attention now turning to Bath City away on Bank Holiday Monday.
Cheshunt Line up
Marsh, Ekongo, Payne, Gardiner-Smith, Frempah, Da Silva, Adams, Re, Liburd, Golding, Reynold. Substitutes: McKenzie, Beckles-Richards, Newton, Miles, McLean.