Stanley had the better chances but the visiting defence held firm.
As early as the fifth minute United goalkeeper Ryan Clarke spilled a Jimmy Ryan high ball into the area and it fell for captain Andy Procter, but Djoumin Sangare pulled off a timely tackle to deny the midfielder a shot at the open goal.
Sean McConville's dangerous cross was almost turned into his own net by United's Paul McLaren. Sean Hessey forced a save out of Clarke from a free-kick while Phil Edwards headed over for the Reds.
In the second half Ian Craney made space for himself but fired straight at Clarke, while the dangerous Ryan went on a mazy run but failed to apply the finish as the Oxford defence dealt with everything Stanley threw at them.
Ryan came close to grabbing the winner late on when he spotted Clarke off his line and tried his luck from 50 yards but the keeper back-pedalled quickly to deny him.