Rye clinched a 39-7 win to remain a point behind a Newick side which currently holds the sole ticket to Division One, while second-bottom Bridge are four points adrift of Ditchling in the Division Two East relegation play-off position.
Rye manager Tony Pierce said: "It was a very good result and very encouraging after a long lay-off (this was their first game in four weeks)."
A sizeable Rye squad actually donated their opponents two players after discovering Bridge only had 13 men shortly before kick-off.
But even though numbers were even, Rye controlled the match pretty much throughout in predictably sticky conditions at Robertsbridge Community College.
Robertsbridge did have a useful pack and stuck to their task manfully, but Rye's powerful forwards with their quick rucking were just too strong.
The New Roaders scored seven tries in all, two of which were converted, while Bridge pulled one back during the second period.
On the scoresheet for Rye were Andy Garrish, Dave Blackman, Eddie Preston, Pierce, Graham Nunn, John Barker and Nigel Jenner on just his second appearance of the campaign. Garrish kicked both of the goals.
Rye will move into the promotion place if they win at eighth-placed Hove III on Saturday March 3 because Newick have a free week.
They are hoping that Jamie Moore will shake off a minor recurrence of his knee problem to leave them with just about a fully fit squad. Kick-off is 2.30pm.
The scheduled visit from leaders Haywards Heath III, postponed two weeks ago due to a waterlogged pitch, has been re-arranged for Easter Saturday (April 7).
But a new date for the arrival of Heathfield & Waldron II is still to be set. The sides were due to meet next Saturday (March 10), but the match has been superseded by Rye's Sussex Shield semi-final against Division One club Burgess Hill.