The away side had every right to feel hard done by, having led for most of the 80 minutes.
First half tries from winger Martin Tarasuik and influential fly half Greg Robinson had given the Bucklastleigh boys a 10-nil lead at the break.
New Cross reduced the deficit to five points when Ali Wellby got on the end of a pass from Tim Prowse to touch down in the corner.
Then, just as it looked as Ramblers would hold on for victory against their higher league opponents, up popped Griffiths to ruin their day.
Tomorrow, New Cross return to Devon One action when they travel to face Salcombe, while Buckfastleigh Ramblers are away to Ilfracombe in Devon Two.MORE SPORT IN OUR DIGITAL EDITION