But if rivals Cambridge win both their remaining games, Roy McFarland's long-time leaders need a point from a tough final game away against Torquay United to be certain - or it could go down to goal difference.
However the Brewers, who at one stage had a 19-point lead at the top of the table, will feel they should already be celebrating life as a Football League club.
For long spells Albion looked like getting the point they so desperately wanted at the Pirelli Stadium on Friday despite chances being at a premium.
Morris tested the impressive Oxford keeper Billy Turley early on and Turley also made a fine block from winger Keith Gilroy.
At the other end, the imposing figure of James Constable forced a good save from keeper Saul Deeney.
The match opened up more after the break after Burton should have gone ahead on 53 minutes.
Burton's Michael Simpson shows his disappointment at the final whistle
Marc Goodfellow's long-range effort forced a fine save from Turley but makeshift striker Darren Stride squared the ball to Morris who completely miscued with the goal gaping.
Oxford made them pay when Chapman's beautifully struck free-kick curled in to the top corner.
United then went down to 10 men when Willmott saw red in the final 10 minutes for fouling Darren Stride.
And in stoppage time Burton's Harrad was red-carded after challenging Turley for the ball during a frantic goalmouth melee.
Burton manager Roy McFarland told BBC Radio Derby:
"I am disappointed for our supporters and everyone who has turned up.
"They can go away looking at how the team played, and I thought they played magnificently.
"It is still in our hands. Cambridge have still got to go and win at Salisbury and if it means taking it on to the last game of the season, we can't do much about it."
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