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Chatham closed the gap on Isthmian South East leaders Ramsgate to just one point after a 2-1 derby win at Faversham on Saturday.
Kevin Hake's side led through Seidou Sanogo's 21st-minute goal at the break. Jack Evans scored his 14th goal of the season to double the advantage in the second half, Kieron Campbell replying late on for Faversham, who are now 10 points adrift of safety.
It was only a second away win of the season for Chatham.
Former Brickies striker Kane Rowland scored against his former club as Ramsgate led at half-time against Sittingbourne.
But Correy Davidson's overhead kick with 13 minutes left ensured a point for new Sittingbourne manager Ryan Maxwell.
Beckenham are up to third following a 1-0 success at lowly Corinthian, Danny Waldren's far-post tap-in on the hour was the difference between the two sides.
Ashford's travel sickness shows no sign of easing as they were beaten for the fifth successive away game, 2-1 at Sevenoaks.
Danny Parish put Ashford ahead midway through the first half but Fumnaya Shomotun equalised on the hour and substitute Daniel Carr scored an 89th-minute winner for Oaks, who are up to ninth.
It's four wins in a row for Sheppey, who edged Hythe 1-0 at Holm Park.
The only goal of the game came with 17 minutes left when Richie Hamill scored direct from a corner beyond keeper Steve Phillips.
Cray Valley's trip to East Grinstead and VCD's home clash with Three Bridges were both postponed due to waterlogged pitches.
Herne Bay's Isthmian Premier match at Kingstonian was postponed due to a waterlogged pitch.
But Kevin Watson's men lost no ground in the race for survival with every other team in action in the bottom eight all losing.
That included Margate, who went down 4-0 at Horsham.
Margate fielded Nathan Wood, who has joined from Tonbridge, but they drew a blank at Horsham, who scored twice in the last two minutes.
Folkestone hit back to claim a point at home to Billericay but were left wondering how they didn't collect all three points.
The visitors scored against the run of play on the stroke of half-time through Brad Stevenson.
But Ibrahim Olutade converted from close range after his header came back off the crossbar with 20 minutes left.
Cray Wanderers, who sit second, host Bishop's Stortford at Hayes Lane on Sunday.