Aaron Rice crossed for Clevedon’s only try of the afternoon while Mike Taylor kicked five points, but the visitors were hindered by ill discipline, which saw them reduced to 14 men on two occasions.
Emosi Tauribau and Aaron Rice were the two players to spend time in the sin-bin, although both decisions appeared harsh.
Drybrook raced into a 14-0 lead with two converted tries, before Rice powered his way through the midfield to reduce the deficit.
But the hosts replied almost immediately with a third try, despite what looked like a knock-on in the build up.
Clevedon went close to scoring a second straight from the kick-off as Will Carpenter latched on to a loose ball following a mix-up in the Drybrook ranks, but his offload failed to find the onrushing Rice.
Taylor kicked a penalty to send the sides into the break at 24-10, but the home side replied with a penalty of their own to extend the lead.
A fourth Drybrook try wasn’t long in coming and a fifth followed shortly after as 14-man Clevedon – with Rice in the sin-bin – struggled to keep the home side at bay.
Harley Foley was a stand-out performer for Clevedon with a typically dogged display, while Rice was constant threat to the Drybrook defence.
The visitors fought to the final whistle but this was very much an afternoon to forget for them and improvement is needed for the visit of local rivals Bridgwater & Albion on Saturday (3pm).