Constable's DVD-inspired form continued for Oxford as he made it two goals in two games.
The 28-year-old claimed a DVD compilation of his past goals had helped him rediscover his best and the unorthodox technique appeared to work as he scored the opener before Sean Rigg added a second to secure a 2-0 triumph for the visitors.
Oxford are nine points ahead of the Football League's basement club and it showed as they dominated proceedings, hitting the woodwork twice in the first half and peppering the Barnet goal throughout.
Andy Whing's cross came back off the bar early on and, as Oxford continued to press, Rigg rifled against the bar with the last kick of the half.
They finally made their pressure pay after 56 minutes as Constable nipped in at the front post to head home from a corner.
Barnet remained toothless as United pushed for further goals and Rigg sealed a deserved win after 80 minutes, drilling home from inside the area.