The match - switched to Hassocks because Gullivers is now in the hands of Sidley Cricket Club - was decided after a quarter-of-an-hour when Tony Hibbert converted a penalty awarded for a foul on the same player.
Also in Division One, Rye United contested a goalless draw away to East Preston.
Westfield continued their push for second spot in Division Two with a 3-1 win at Storrington, the damage being done by Dominic Clarke (2) and Lawrence Brand.
An 89th minute finish from Lewis Hole gave Little Common a 2-1 success at home to Hurstpierpoint in Division Three. Kingsley Parsons had levelled a minute after the Commoners had fallen behind.
A busy week of County League football starts with Sidley's visit to Hailsham Town on Monday April 23 (7.45pm). The next day Rye travel to Ringmer (7.45pm), Westfield make the trip to Steyning Town (7.45pm) and Little Common take on Bexhill United at the Recreation Ground (6.30pm).