Put into bat, Rye recovered from the early loss of Martin Barry thanks to James Hamilton (52) and Mark Cook (36) who shared a stand of 70.
Although they hit the ball with great fluency, scoring was restricted by a slow outfield and the nagging bowling of Steve Cornford (0-25 off 13 overs) and Ricki Horne (2-42 off 15 overs).
The demise of this partnership saw Martin Menezes (36 not out) take command and steer Rye to 193-6 and eight batting points as he shared good knocks with Gary Osborn (16) and Dan Brownbill (31).
Richard Melbourn (2-28) grabbed some consolation bowling points for Ramblers at the end of an innings which took nearly three hours to bowl 50 overs.
Ramblers made a stuttering start to their reply before rain made conditions difficult for batsmen and fielders alike.
Despite Peter Winchester hitting 34 the visitors were never in a position to win the game and were eking out time to gain the draw. The high point at this stage was a steepling catch taken by colts player Peter Stonham.
The score was 118-5 with nine overs remaining when Gandhi Tandoori man of the match Martin Blincow (4-35) bagged two wickets in two balls and Mark Cook (2-18) struck at the other end with a caught and bowled.
Cook claimed another wicket but Ramblers hung on in the gathering gloom to finish on 130-9 thanks to an undefeated 43 from Ali Burnett.