Relegation-threatened Margate are five points from safety after losing at Carshalton in Isthmian Premier on Saturday.
It’s now nine defeats in 10 games for Mark Stimson’s men who have just eight games left to rescue their season.
Goals from Kwaku Frimpong, Charlie Kennett and Luke Read did the damage.
A stoppage-time equaliser from Ashley Nzala gave Chatham a point at 10-man Hastings.
The hosts had Tommie Fagg sent-off with 20 minutes left but went ahead through a Simon Cooper own goal in the last five minutes.
Tom Derry’s second-half goal was the difference as Folkestone moved 14 points clear of the bottom four with a 1-0 home win over Canvey Island.
Cray Wanderers announced the sad death of former club secretary Kerry Phillips ahead of their trip to Haringey Borough, and promptly put on a fitting show in his memory to run out 4-0 winners.
Haringey were reduced to 10 men after 16 minutes when Nadum Melvin-Lambert saw red with goals from Ellis Brown, David Ijaha, George Porter and Anthony Cook doing the damage.
It’s as you were at the top of Isthmian South East after leaders Ramsgate and second-placed Cray Valley both won.
Joe Taylor’s penalty took his personal tally for the season to 40 goals before TJ Jadama added a second on the stroke of half-time at Burgess Hill, who pulled one back in the second half.
Cray Valley had a goalless first half at Sheppey but took just 12 seconds to take the lead after the break through Sonny Black.
They wrapped the points up in front of anther bumper Holm Park crowd – 802 were in attendance – when Black netted again with 16 minutes left.
Sittingbourne lost ground on the top two after losing 1-0 at home to Broadbridge Heath.
Herne Bay recovered from conceding two goals in the first nine minutes at Merstham to draw 2-2.
Harry Pointing and Lorenzo Lewis put the hosts in charge but Vance Bola’s second-half brace ensured Bay took a point on their travels.
Frannie Collin’s late penalty rescued a point for Hythe at home to Three Bridges, who led through Nabeel Ghannam midway through the first half.
Robbie Rees’ first-half goal was the difference as Ashford United ran out 1-0 winners at home to Littlehampton Town.
Kieron Cadogan’s second-half equaliser saw Sevenoaks draw 1-1 at home to Beckenham, Phoenix Sports were held to a goalless draw by East Grinstead while Erith & Belvedere went down 3-1 at Lancing.
