United were forced to play for just under an hour of the game with ten men after Danny Simmonds was sent off after conceding a penalty which led to Midhurst's first goal.
The game had started brightly for United with the prolific Liam Baitup taking just seven minutes to open the scoring as United looked to build on last weeks victory over champions-elect Littlehampton Town.
Baitup doubled the lead on 18 minutes after Jack Mclean beat the offside trap to set up the divisions leading marksman for his second of the match and league goal 35 of the season.
The game turned on 35 minutes with the dismissal of Simmonds and from the resulting penalty, Lewis Hamilton dispatched the ball past Adam Sargent to bring the hosts back into the game.
Despite their numerical disadvantage, United held on to their lead until the 60th minute as Luke Sheldrick pulled the hosts level.
The result leaves EUAFC third in SCFL Division Two, a point ahead of fourth placed Little Common who have a game in hand.
With both of United's remaining league fixtures against Loxwood this coming Saturday (3pm) and Rustington to be played at The Oval and with Little Common to face Littlehampton Town on the final day of the season, the race for SCFL Division One looks set to go down to the final day.