The goal came from the kick-off in the second half, with Andrew Teague failing to clear an easy ball allowing Basham to score at the second attempt against the unprotected Alan Fettis.
Oxford had dominated the opening exchanges and were unlucky when Basham saw a 20-yard volley crash back off the post in the 13th minute. Chris Hargreaves and Lee Mansell then sent golden opportunities wide of the target.
Macc should have scored in the 26th minute when Martin Bullock dashed on to a long ball from Danny Swailes only to hesitate in front of goal allowing Chris Tardif to save bravely at his feet.
They eventually broke the deadlock on 37 minutes when Tardif could only parry a Clyde Wijnhard bullet into the path of Kevin McIntyre who gleefully stroked home his third goal of the season from close range.
Bullock and then Wijnhard both saw chances cleared off the line as Macclesfield failed to press home their advantage. They were made to pay moments after the break as Basham pounced on the young centre-back's mistake to leave manager Brian Horton fuming on the side lines.
Eight minutes later Basham should have given Oxford the lead but having side-stepped the defence he planted a 12-yard shot inches past the far post.
The Cheshire side were unlucky in the 75th minute when a rasping long range drive from left back Kevin Sandwith cannoned off the cross bar.