They had the majority of possession and with 25 minutes to play Thame had a 1-2 lead.
Their eventual defeat at the hands of a team from a lower division was the result of some sloppy defending and poor finishing.
Thame had a good chance after 16 minutes when Darren Moore found himself five yards from goal and in a one-on-one with the home team's goalkeeper, but he took the season of goodwill too far when his shot hit the delighted keeper.
Rayners Lane took the lead in the 38th minute after Thame goalkeeper Paul Searl had parried a shot which Ian Jones collected and fired home.
Moore equalised for Thame on 45 minutes with a strong 20 yard shot low into the left corner of the home goal.
Thame took the lead eight minutes after the restart when Nathan Jack made a quality run to the left by-line before hitting a low cross which the goalkeeper fumbled and Adrian Smith tapped in.
Rayners Lane equalised 15 minutes later when Jones netted his second from close range following a defensive mix up.
Thame continued to have more of the play but frustratingly squandered their goal scoring chances.
With 15 minutes remaining, the home side made a rare trip into the Thame half and Jamahni Henry beat Thame goalkeeper Searl with a blistering 25 yard shot to give Rayners Lane the lead.
The last few minutes saw relentless pressure on the home goal with at least two goal-line clearances.
Searl joined in the attack and Thame could have been awarded a penalty when a defender looked to have blocked a shot with his hand.
The referee, however, did not see the infringement and a few seconds later blew the final whistle.
Thame United: Searl, Tripp, Watkins (Da Silva), Bell, Kitson, Cairns, Jackson (Reading), Moore, Smith, Jack, Ricketts.
Result: Rayners Lane 3
Thame United 2