The opening 20 minutes proved a cagey affair littered with penalties from both sides.
But the hosts took the lead early in the second quarter following a spell of sustained pressure, hooker Harry Bicknell burrowing over from close range.
Ross McKay – who impressed at fly-half along with fellow newbie Matt Wickham inside him – slotted a simple conversion.
There were few other scoring opportunities before the interval, the defences on top with Mikey Duda his usual dynamic presence in the back row.
A completely new 15 lined up for Rams in the second period, and they extended their advantage thanks to a try from skipper Willo Bicknell.
After Clifton spilled the ball in midfield Henry Kirwan smashed a long kick downfield, Connor Burns providing the initial pressure before Bicknell ripped the ball to dive over.
Darren Atkins was narrowly off target with his touchline conversion attempt, and Clifton cut the deficit soon after.
Andy Thomas was the beneficiary of a huge maul, grounding on the left before Tom Quinlan slotted a fine conversion.
Hosts pull clear in final quarter
But former Bath man Atkins then produced a moment of magic.
Collecting a clearance kick on halfway, the fly-half showed an explosive turn of pace to scorch past a couple of would-be defenders before diving under the posts for a sensational try.
He added a simple conversion and then one far harder after more strong work from the pack was finished by Aron Tull on the left-hand touchline.
The hosts then made the game safe with the team try of the afternoon, Ellis Jones initially with a deft flick to send his side hurtling forwards.
And Ryan Lomas then off-loaded to Seb Burgess, the substitute diving over before Atkins added the extras.
Clifton refused to give up, though, and grabbed a second score as wing Henry Leigh cut a nice line before finishing for a converted try.
But it was Rams who had the final word, Theo Pett-Ridge with a well-read interception before racing home from 30 metres out.
Seb Reynolds’ side travel to Aberavon next Saturday (2.30pm), with the National One season starting at home to Sale FC on September 5.
