It was the perfect start for the U's when they went ahead after just one minute as
Ross Flitney wanted too much time in controlling Anthony Charles's back-pass as French striker Eric Sabin closed him down. The ball ran to Tcham N' Toya who calmly slotted the ball underneath the keeper as he tried to get back.
It was the worst possible start for the Bees, who were just below Oxford in the table. And life got worse as they fell two goals behind on 25 minutes.
Hargreaves headed Jay Smith's cross forward and N' Toya chested it down and beat his marker before driving low past Flitney for a brilliantly-taken goal.
It was the first time since Boxing Day that the U's had managed to get two goals in one game.
No-one in Oxford was under-estimating the importance of this match. With difficult games coming up against promotion-chasing sides, the U's, now managed by Jim Smith, were facing the very real prospect of losing their Football League place after a 44-year stay.
Oxford's preparations for the game were not helped by Italian keeper Andrea Guatelli picking up an injury during the kick-in. He had to be replaced by Billy Turley, who hadn't played for a month.
Smith played three strikers in a 4-3-3 formation, with N' Toya and Sabin supported by Steve Basham.
Charles sent a difficult left-foot volley over the bar at a corner and Turley had to turn a tricky bouncing shot from Paul Warhurst aside for a corner. But at the other end Flitney and his defenders looked very uncomfortable every time Oxford put them under pressure, and when the keeper had to deal with another difficult back pass, he booted the ball into touch.
Barnet must have been given a dressing-down at half-time from manager Paul Fairclough because they came out for the second half much more fired up.
Nick Bailey went close with a 25-yard free-kick and later in the half Bailey had a fierce drive well blocked by Leo Roget.
Oxford midfielder Jay Smith was booked for a professional foul on Paolo Vernazza as the Bees fans screamed for Smith to be sent off, but there had been covering defenders.
The U's almost got a third goal near the end when Hargreaves's pass over the top set substitute Jamie Brooks free, but the striker was let down by a bad first touch.