Rovers were no match for in-form Thurrock as the visitors hit four goals to take the points.
Rovers had pulled level early in the first-half through Tom Ranger but Fleet were well worth the points, with David Cowley particularly impressive in the middle of the park.
Charlie Stimson had opened the scoring inside the first 10 minutes, with Mark Stimson’s team pressing at a high tempo.
Neat work down the flank saw the ball crossed to Stimson and he made sure from close range.
But the lead didn’t last long. Ranger capitalised on a goalkeeping error from Rhys Madden and tucked home.
Back came Fleet and they again went in front with a sublime goal. Cowley picked up the ball to crash home a delightful effort.
The two teams exchanged blows as the half went on but the third goal didn’t come until after the hour mark.
Former Rovers man Ross Wall got the third goal with 64 minutes played and Jordan Clark made sure from the spot following a handball from Rovers skipper Lewis Sparrow.