Fleet took full advantage of some early possession to take a 2-0 lead on 24 minutes.
The first from the penalty spot after a Spurs player cut inside following a fine run down the left side, was brought down in the Hook penalty area.
The second, also scored by Dan Bone, when the striker met a crossfield ball from the right to slot home inside the visitors left hand post.
Seven minutes later Spurs could have extended their lead but the ball chipped over the keeper was also just over the bar.
Hook upped their game and pressed Spurs with several attempts on the home side’s goal, which Jordan Vincentin goal made a string of fine saves - including a double save from close range.
The pressure finally resulted 3 minutes into first half added time, when a strong shot from a Hook attacker managed to slip under the home keeper.
The second half can be summed up as, Hook pressure vs Fleet Spurs stalwart defending.
Fleet Spurs earned these well deserved 3 points against an organised and committed Hook side promoted from HPFL Division 1 last season.