The U’s had won all four previous home games this campaign, including three in the league, while the Clarets were in good form after recent victories at Leeds and against Portsmouth.
In a game of few clear chances, Scott Parker’s men went close with Jamie Cumming tipping Luca Koleosho’s effort over the bar early in the second half.
And hard-working Oxford almost grabbed victory late on when Tyler Goodrham saw his low shot blocked on the line by Maxime Estève.
These clubs were two divisions apart six months ago but Oxford, who won promotion from League One through the play-offs, did not appear overawed by the opposition players, many of whom were playing in the Premier League last season.
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