Thame boss Mark West was left bitterly disappointed on Tuesday night, after seeing his side twice surrender the lead to settle for a draw.
In an entertaining clash at the ASM Stadium, United missed the chance to pull clear of the visitors, who sat four places below them in the league, thanks to a last minute strike.
The side started brightly and had the better of the first half, with Thame keeper Milan Barisic mainly a spectator.
Ben Connelly was a constant threat on the right wing before the visitors countered his pacey, tricky runs by allocating two men to mark him.
United took the lead in bizarre fashion in injury time at the end of the first half.
The ball came in from the right and Stuart Barr, with his back to the goal, tried a spectacular Rooney-like scissor kick, which was deflected out for a corner.
Barr took the in-swinging corner which eluded goalkeeper, defenders and forwards alike before crossing the goal line.
Perhaps it was a lucky fluke, but no more than Thame deserved.
The visitors came out fired up for the second half and in the 50th minute were awarded a free kick on their left.
The ball came in high and Barisic went to collect it but the greasy ball slipped from his hands to fall at the feet of a visiting forward.
Barisic then tried to reclaim it but was judged to have fouled the forward and the referee pointed to the penalty spot.
Sam Collier buried the resultant spot kick, giving Barisic no chance.
The home side regained the lead in the 59th minute when Ben Connelly found Alex Stewart on the right of the area.
The in-form Stewart coolly turned and hit a well placed, acutely angled, 20-yard shot pass the visiting keeper.
The visitors came back, and Barisic was forced to make an outstanding save, tipping a strong shot over the bar.
With a minute to play, just when it looked like Thame would hold out, a long ball from the left found substitute Alex Green in space and he beat Barisic with an eight-yard shot.
Next up for Thame is a tricky home clash with Highworth Town.