United fell behind on five minutes when Sam Knowles found the right corner from the penalty spot.
The next fifteen minutes saw Woodley have plenty of the ball but struggle to link midfield and attack.
It took till the twentieth minute for United to create their first clear chance. Charlie Oakley and Greg Beckett combined with the latter forcing the Fleet goalie into a routine save. Sixty seconds later, Woodley were once again denied by the home keeper.
The half ended with the sides trading shots; Knowles prodded a good chance wide before Oakley was denied by the Fleet keeper. The final chance of a half Woodley dominated from a possession point of view saw Toby Briggs shoot well wide from distance.
HT Fleet Spurs 1-0 Woodley United
The second half got underway with Danny Greenwood picking out Oakley with a superb pass; going round the goalie the United forward hit the outside of the post from a tight angle.
Woodley pressed on, a nice move started after a neat turn by Callum Samuel-Harmen ended with the home keeper once again thwarting United.
The scores were level with thirteen minutes left when Oakley turned home from close range after Michael Porter headed a right wing corner goalwards.
With the game in its final ten minutes, United hit the outside of the post for a second time. Good link up play between Marvin Hinds and Beckett ended with the former having his shot deflect off a Fleet defender and clip the woodwork.
Woodley had a real let off with two minutes left when the hosts should have nicked a winner. A low cross from the right found a Fleet forward unmarked six yards out; mis-controlling the ball, it allowed Alex Reed time to close the angle and save before the ball was cleared.
The miss was to prove costly as United won it at the death when Oakley headed in a Nat Robinson corner.
FT Fleet Spurs 1-2 Woodley United