England had trailed 15-6 when Ivybridge fly-half Pinkus came on for his international debut.
He helped England move 21-15 ahead, with a penalty and a conversion.
But in the dying minutes England had former Barnstaple player Hallam Chapman sin-binned and while down to 14 men they conceded a penalty try to go 22-15 down.
However, with the last play on the game Georgia gave away a penalty and had a player yellow carded. The penalty was 40-metres out and near the touchline. Pinkus, though, had the confidence to go for goal and he put it over to win the game for England and take his tally for the afternoon to eight points.
The victory meant England Counties Under-20s ended their tour unbeaten having beaten Georgia’s Under-20 World Cup side 24-17 last weekend.