With Thame reduced to ten men after just half an hour, the visitors took the lead early in the second half through Seb Bowman before the same player doubled their advantage 78 minutes.
Despite the deficit, United had always looked dangerous and they pulled a goal back on 81 minutes through Andy Gledhill.
Captain Ellis Hercules then secured a point on 85 minutes, turning sharply in the box to beat the keeper at the near post.
Thame are currently fifth in the Hellenic Premier Division and host
Two young players who have played a part in Thame’s recent revival are midfielder Tom Ashworth and right-back Charlie Attwell.
The two 18-year-olds both graduated into the first team having impressed for the academy.
Academy coach Craig Faulconbridge said: “Both have really excelled over the last 18 months, leading to a number of first team opportunities.
“Tom actually played against Oxford United in a pre-season game, and he’s been in and out of the team since the start of the season.
“Recently, however, he has nailed down his place and Charlie has followed a similar path really in terms of being in and out of the side.
“I think it’s how the manager operates in terms of blooding young players, gives them a taste of first team action before taking them out for a while, and then putting them in permanently.
“It’s really important for the club to have local talent coming through and people who are from the local area.
“Trials for the course which starts in September take place on Tuesday, March 29, and Tuesday, April 5, so if there are guys at U16 level who want to come on and play football alongside their studies it’s a good opportunity to show us what you can do.”
“The future’s looking bright for both the academy and the first team in terms of people coming through the ranks.”