Whitstable scored twice at the death to move 11 points clear in the Southern Counties East Premier Division.
Struggling Stansfeld took a second-minute lead through Glen Bain and it looked set to stay that way until a dramatic late turnaround after the hosts had Oliver Andrews sent off.
Javaun Splatt levelled on 88 minutes and Bradley Schafer’s last-minute winner earned a 2-1 victory for Jamie Coyle’s league leaders.
They extend their advantage over second-placed Larkfield & New Hythe, who were without a game.
Rusthall consolidated third place with a 3-1 home win over Kennington.
Louie Clarke’s early opener and a second-half double from Charlie Clover put the home side in charge, with Ryan Philpott replying for Ton.
Bottom side Hythe produced a stirring late fightback to draw 3-3 at home to Punjab United.
Taurean Roberts’ early penalty edged the Cannons in front but Punjab struck three times in five minutes through Jack Hopkins, Jordan Campbell and Anthony Adesite to take control after the break.
Steadman Callender gave Hythe hope on 83 minutes and Mo Kamara levelled three minutes later as Darren Beale’s side drew level on points with Stansfeld.
Corinthian were the day’s biggest winners, claiming a 5-2 victory at Faversham Strike Force.
Tom Mitcham, Caleb Afoke, Jack Billings, a Harry Earls own goal and Akshar Santhosh’s injury-time goal made up the visitors’ tally.
Alex Willis briefly drew Strike Force level at 1-1, while Mefose Esumobi scored their second in added time.
Sutton Athletic moved up to fifth with first-half goals from Omotunmise Akanni and Conor Evans in a 2-1 away win over Hollands & Blair, for whom Dieko Falade replied in first-half injury time.
Holmesdale dropped to sixth on goal difference following a 2-2 draw with Erith & Belvedere.
The Deres led twice, Ronnie McClean and Alfie Morgan on target, but Lewis Heywood-Oriogun and an injury-time Deandre Williams goal secured a point.
Snodland and Fisher cancelled each other out in a goalless draw between sides level on 31 points in eighth and ninth.
