Restored to the starting line-up by manager Chris Wilder, he missed two great chances in the first half, denied on both occasions by home keeper Michael Poke after racing onto passes from Alfie Potter.
However, he was on target in the 50th minute as he rounded Poke before sidefooting the ball home. Four minutes later Damien Batt doubled the lead from the penalty spot after Constable had wriggled clear of Aaron Downes only to be brought down by Torquay's big Aussie defender.
Downes redeemed himself with a goal to put Torquay back into the game in the 58th minute, guiding in a far post header from a Kevin Nicholson corner.
And Oxford's third goal came with the last kick of the game as Simon Heslop broke away on the right of a stretched home defence and drove the ball low past Poke.