Wrexham moved into the Sky Bet Championship play-off places as in-form Josh Windass pushed Oxford closer to the relegation trapdoor.
Top scorer Windass gave Wrexham a precious 1-0 victory with his fifth goal in six games five minutes before the break.
The win saw Wrexham take sixth spot from Hull on goal difference as the Tigers were held 2-2 at Leicester.
Wrexham's hopes of making the play-offs - and possibly a historic fourth consecutive promotion - now rest on closing fixtures against champions Coventry and fifth-placed Middlesbrough.
It is a much different story for Oxford, who face the distinct prospect of joining Leicester and Sheffield Wednesday in League One next season.
The Us will be relegated on Wednesday should Charlton draw against Ipswich and Blackburn beat Sheffield United.
Before kick-off Oxford showed footage of the 1986 League Cup final - in which they beat QPR almost 40 years to the day - on the big screen to get fans in high spirits.
The home crowd's mood almost improved further when Myles Peart-Harris and Will Lankshear nearly got on the end of Sam Long's cross, but Wrexham soon began to carve out chances after a cagey opening.
Sam Smith's every touch was barracked by Us fans with long memories of his loan spell at the club in 2018-19, but the forward almost silenced those jeers when stretching and diverting George Thomason's cross just wide.
Dominic Hyam headed over Thomason's corner at the near post and Windass flashed wide from a rapid counter-attack before Wrexham seized command.
Smith battled well to lay the ball into the path of Windass and his unerring low drive from 20 yards gave him his 15th league goal of the season.
Oxford had huffed and puffed but created little of note until Stan Mills' goalbound effort was blocked by Thomason just before half-time.
The energetic Mills helped Oxford build up an early second-half head of steam and Michal Helik's header was collected by Danny Ward on his line.
But the hosts were fortunate to survive when Callum Doyle climbed well at the far post and his defensive partner Hyam was kept out by the reflexes of home goalkeeper Jamie Cumming.
Mills saw his header deflected over and Hyam's decisive touch close to the goal-line on prevented Lankshear from profiting at the far post.
Oxford exerted late pressure but Wrexham's defenders stood tall and Ward held on from Aidomo Emakhu in stoppage time to keep the dream of Premier League football very much alive.
Oxford's Matt Bloomfield:
"The boys gave everything they've got and we're really frustrated we couldn't give the crowd what they wanted.
"We're all feeling it right now and it's understandable because the fans care about their club so much.
"But we have to wear it and bounce back and come Saturday we have to be full of energy as a football club.
"I don't enjoy where we are in the league. It's not comfortable, but that's the reality and we have to attack the game on Saturday."
Wrexham's Phil Parkinson:
"The (Premier League) dream is still alive and we feel we're in a good place.
"Nothing more we can do than win and we just concentrated on making right decisions from the bench and getting another three points.
"To get 70 points is a good statement in our first season in the Championship and now we want more. It was important we did our job, and we did that to a man.
"We showed two sides to our game. First half we had really good control in the game, we were patient and took care of the ball.
"The moment came and we had chances second half, but we knew Oxford would throw caution to the wind. They're fighting for their lives.
"Long throws, set-pieces, and we defended as a team. Everyone did their job."
