THURROCK made it back-to-back wins, while Tilbury suffered a heavy defeat at Dereham Town on Saturday.
Fleet travelled to Kingstonian on the back of a 1-0 success against Harlow Town on New Year's Day.
And Mark Stimson's side were able to claim another 1-0 win at Fetcham Grove.
Joe Christou scored what proved to be the only goal on the half hour mark.
The midfielder found the back of the net with a superb 25-yard free kick, which gave goalkeeper Rob Tolfrey no chance.
Christou's breakthrough came after Fleet goalkeeper Ben McNamara thwarted Andre McCollin on two occasions.
McCollin was denied yet again just before the break as he was ruled offside before rolling the ball into the net.
Marvin Elliott struck the post after the break, but Kingstonian could not find a leveller.
As a result, Thurrock were able to return to Ship Lane having kept their perfect 2018 record intact.
Fleet now find themselves in 13th place in the Isthmian Premier League standings.
Meanwhile, Tilbury lost 3-0 to Isthmian North promotion chasers Dereham Town.
James Cooper gave the Magpies a 10th minute lead, before doubling his and his side's tally on 38 minutes.
The Dockers were hoping to stage a second half comeback but Jamie Forshaw put the result beyond doubt when he converted with 15 minutes to play.
Tilbury are 17th in the Isthmian North standings ahead of their trip to Bowers & Pitsea on Tuesday.
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