George Francomb was sent off as Crawley Town made it three defeats in three in this year's EFL Trophy.
Gabriele Cioffi's men were already out of the competition while Oxford had it all to play for. Cioffi selected a much-changed side with Joe McNerney, Jamie Sendles-White and Denzeil Boadu all getting starts.
The visitors took the lead after just 10 minutes after David Sesay got caught in possession leading to Oxford driving forward and Rob Hall slotted through the legs of Michael Luyambula.
The Reds bounced back after going a goal down and Ashley Nadesan had a good shout for a penalty turned down.
But it Oxford who scored next after McNerney conceded a handball inside the area and Anthony Forde converted the penalty.
Crawley got a goal back six minutes after the break. After a scramble inside the Us box after some good work from BezLubala out wide. His, Ashley Nathaniel-George and Boadu's shots were blocked before Mason Bloomfield headed home.
But the comeback was short-lived as Reds conceded another penalty as Mark Sykes dispossesses George Francomb who then pulls him back in the box. The defender was shown a red card for the foul before Hall got his second from the spot.
And it was Hall who completed his hat-trick - again from the spot after Luyambula brought down Agyei.
There was a bit of history for Oxford in the 80th minute when at 16 years and 98 days Tyler Goodrham became United's youngest player since joining the club turned professional in 1949, beating Graham Atkinson's previous record.