Tries from Harley Foley, Josh Mortimore and Tom Thie, plus 15 points from the boot of Mike Taylor, condemned the visitors to only their second defeat of the season – after Cleve hooker Neil McMahon was sent off in just the tenth minute for a stamp.
Flanker Foley granted his side the perfect start to the game as he scooped up a loose ball straight from the kick-off to gallop in from 20 metres.
Taylor added the first of a spotless display from the kicking tee to give the hosts a 7-0 lead – and things got even better for Clevedon on ten minutes when McMahon received his marching orders following an incident at a ruck.
Clevedon took full advantage of their numerical advantage as scrum-half Mortimore, who impressed throughout the afternoon, sniped his way over from close range after a powerful carry from centre Dave Price.
Taylor added the extras from under the sticks, before extending the lead further with a well-struck penalty.
But the league leaders certainly weren’t going to go quietly and responded shortly before the break with a try from Brad Kislingbury - Roberts converted to send the sides into the break at 17-7.
Cleve pulled themselves right back into the contest just minutes into the second-half, as Sean Lilley crashed over to bring his side within three points.
Clevedon responded with Taylor’s second and third penalties - and soon crossed for their third try of the afternoon, with Thie latching on to an outrageous offload from Mortimore to put the hosts 30-14 ahead.
But it was a far from comfortable final period for Clevedon, with both Owen Biggins and Mike Taylor spending time in the sin-bin as Cleve enjoyed their first numerical advantage of the game.
Craig Owen and Lewis Beer crossed for tries in the latter stages, both converted by Roberts, to make it a two-point game and ensure a tense finale – but the hosts held on, showing the type of steely determination required to turn their season around.
Fittingly, it was man of the match Mortimore who dispatched the ball from the field of play to signal the final whistle and secure a third league win of the season for Clevedon.
Next weekend, Clevedon travel to Wells looking to build on this result.