The defeat means that Tranmere have now lost five straight league games and stay bottom of the table.
Oxford took the lead in the first half as Barnett returned from suspension to score only his third goal in 41 games.
Danny Hylton picked up the assist after linking up with the forward neatly.
Potter sealed the victory with 15 minutes left as Joe Riley's cross was picked up in the box and rifled into the bottom right corner.
The victory is Oxford's third in their last six games and sees them climb to 20th.