Hackett was shown a straight red card after he kicked out on the ground at Tony Craig.
It left Oxford with a man short for the second time in a week because they had lost Tommy Mooney at Rushden on Boxing Day.
Jamie Brooks grabbed his first goal for nearly three years since being sidelined with the life-threatening illness Guillain-Barre Syndrome.
He drove low under the body of keeper Frank Talia from Mooney's lay off.
It needed three great saves from Chris Tardif to keep Oxford in front, his best coming when he tipped Nathan Tyson's header against the bar and then smothered the loose ball as Wycombe players ran in.
Substitute Steve Basham put daylight between the two teams when he extended Oxford's lead three minutes from time, deflecting in a long-range free-kick by Lee Molyneaux.
But Wycombe gave themselves a glimmer of hope by pulling a goal back in injury time.
Barry Quinn was adjudged to have fouled Danny Senda, who picked himself up to convert the penalty.
And with almost the last kick of the match, Craig Faulconbridge headed a corner into the Oxford goal for what he thought was the equaliser only for the referee to disallow it for pushing.