They trailed 13-7 at half-time, with a converted try by flanker Lee Worgan being their only reward for some great forward play.
In the second half, two sin bins were to cost the side a valuable away win. Weston showed a great deal of flair and were able to exploit the one-man advantage for a significant part of the half.
A cleverly worked move put stand in full-back Ben Care into a gap which he managed to capitalise upon to reach the line. This try gave the visitors some hope of coming home with something from the game. Eventually the Weston made their numerical advantage count and ran away winners.
Gordano will hope to return refreshed on Saturday when they entertain Old Reds at Caswell Lane.