United were already in the driving seat courtesy of Sean Rigg's 13th-minute goal when McGuire was sent off for a two-footed tackle on the U's midfielder.
In eight minutes of first-half stoppage time, the 10-men levelled through Lee Stevenson only for substitute James Constable to bag his 100th Oxford goal within two minutes of coming on.
Ryan Williams' 66th-minute strike, crowning a great performance, then sealed Oxford's 3-1 victory.
Although Stags put eight past St Albans in the FA Cup last weekend, Stevenson's goal was their first in 472 minutes of league football and they are now seven games without a win in League Two.
"The game changed with the dismissal," said boss Cox. "It's hard enough to play with 10 men against any team, let alone a team like Oxford, who have been in the top three all season and have a great away record.
"We gave ourselves a mountain to climb.
"I will have to see the red card again on DVD. I thought both boys went in for a full-blooded tackle. The referee said it was a two-footed tackle.
"With Jamie you are always going to get incidents like this as he wears his heart on his sleeve and gives his all for the club.
"We have to learn from this. Referees have a hard job and if you go in with two feet or any kind of foul play you are going to be shown a straight red.
"With 10 men we worked hard and kept our shape. And we probably created the three best chances in the second half. But all three of the goals we gave away were sloppy."