A fourth minute goal from striker Ed Smith earned Fleet a deserved point and should ensure Ryman Division One football at Calthorpe Park next season.
But with the other relegation rivals, Ashford Town and Dorking also taking points from Saturday's games, Fleet's fate will not now be finally decided until the final league matches next Saturday.
Fleet have a tough visit to fifth place Met Police, but at least have the points on the board - being three points clear of Dorking. Both Ashford Town and Dorking go into their respective matches at Horsham and Whyteleafe, knowing they have to win to avoid the drop - a draw or defeat for either side could mean the drop, and Fleet would be safe whatever happens at Imber Court.
Fleet led for most of Saturday's match against third place Horsham after Smith followed up on a low, long-range effort from Phil Archbold. Archbold's shot was not taken cleanly by Horsham keeper, Luke Burton in the wet conditions, and Smith was on hand to tap in. It was a fortunate start for the Fleet side, after the ball was mis-cleared from the Horsham defence, hitting referee, Robert Smith on its way to Archbold.
But Fleet responded well to their early good fortune and played enterprisingly well for the rest of the half, creating plenty of opportunities for their front men, Smith and impressive debutante, Nathan Smart. For their part Horsham looked slow in defence, but were threatening in the box, wingman, Gary Chapman going close with several excellent headers.
It was Chapman who then had Horsham's best chance just after the break, but from close range his shot somehow went wide. On 55 minutes Smart could have made it 2-0 for Fleet, after a great pass from Smith, but Burton gathered the youngster's shot easily.
Fleet's early advantage was then squandered when Smith was sent off in the 65th minute for a second bookable offence. Having been booked earlier for a reckless challenge Smith was then shown red after ignoring the referee's whistle, leaving his side to play out an anxious final 25 minutes.
With Fleet then reduced to ten men, Horsham immediately equalised, Chapman at last finding the target with his head, after a great cross from the right.
Horsham went all out for the winner, but Fleet defended well, and held on to take the vital point they needed.
