The United stopper first denied James Collins, before bravely diving at the feet of Adam McGurk to claw the ball to safety.
Potter went close half-way through the first period but his effort was gathered by Elliot Parish in the Villa goal.
The hosts took a grip on the game and, having dominated the midfield battle, they were rewarded on 37 minutes when the youngster opened the scoring.
Rhodes did well to hold off his marker before cutting the ball back to Potter who finished neatly from 10 yards.
Just seven minutes later, United's lead was doubled when Rhodes linked up with Potter again; the latter steering the ball expertly inside the far post.
Villa almost got back into the game just after the break, but Gary Gardner failed to keep his header down when well placed.
Potter continued to be at the heart of all that the home side created and his cross was almost diverted into his own net by Daniel Devine.
The game may have been a friendly but tempers flared on the hour-mark after substitute Deering mistimed a tackle on Gardner, with the U's player shown a yellow card and Gardner being forced to leave the field through injury.
Both sides had half-chances in the closing stages of the match with Chris Herd floating a free-kick just wide for the visitors and Marcus Kelly coming close to a third for United.
The final whistle marked a thoroughly deserved 2-0 win for the U's and the end of their pre-season games ahead of the start of the Blue Square Premier campaign, which kicks off against York City on Saturday, 8 August.
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