Woodley's first opportunity came from a free kick just outside the Thame box after a foul on Rupen Limbu. Nathanial Robinson stepped up for the set piece but missed to the left. This chance was sandwiched between two long range efforts from the visitors who were seeing plenty of the ball in the opening stages.
Fifteen minutes gone and Woodley nearly went ahead when a Robinson corner found Fraser Mowat; the midfielder struck his shot well only for a Thame player to clear from practically the goal line.
It was then Thame's chance to go close from a set piece. A corner from the left was headed goalwards but tipped round the post by Woodley stopper Harry Stiff. Mid way through the half saw the visitors go ahead when Woodley captain Luke Titcombe bought down Luke Ricketts in the box. Up stepped Dan West who coolly sent Stiff the wrong way with a shot to the bottom right corner.
Moments later, a run down the right wing by Thame's Calvin Evans saw Stiff again called into action to deal with a dangerous low cross. The away side then came within inches of doubling their lead when a shot from outside the box cannoned off the bar.
The half ended with more Thame pressure; a cross from the right went through a host of players before finding an attacker who forced Stiff into another decent stop.
HT Woodley United 0-1 Thame United
After the break Thame continued to dominate. First the visitors were denied by a great block at the back post, then Stiff saved at the second attempt following a vicious free kick.
Just before the hour, Mark Ingram replaced right back Zack Pearce in a straight swap. Then, against the run of play, Woodley nearly equalised when a Mowat half volley clipped the left post.
Two quick chances for Thame followed; first Stiff bravely punched clear a low cross from Evans, the ball fell to Tom Ashworth who saw his firm shot well saved.
With twenty minutes to go Woodley forced Lee Farrow in the away goal into his first real action of the game. A deep Thame free kick was cleared to Limbu on the half way line; driving into opposition territory he saw his shot from twenty five yards saved in the left corner.
Minutes later Thame sealed progression to the next round when a miss communication in the Woodley defence allowed Andy Gledhill to ghost in, round Stiff and roll the ball into an empty net. Before kicking off, Woodley made their penultimate change when Mowat was replaced by Joseph Danelian.
With the game winding down, Woodley made their final change; Graham High came on for Ryan Szram. The game's final chances fell to the visitors. First Titcombe made a brilliant recovery to block a Ben Gray shot, then a beautiful right wing cross somehow evaded the head of a Thame forward.
FT Woodley United 0-2 Thame United