Marlon Pack came agonisingly close for the home side, but his superbly struck free-kick came back off the woodwork.
Darryl Duffy was unlucky with a six-yard header which was tipped over by Oxford goalkeeper Ryan Clarke. James Constable headed over and at the other end Ben Burgess volleyed wide from 12 yards as the chances continued to flow.
Marlon Pack had the best chance of the first half in the 43rd minute. Damian Batt brought down Luke Garbutt 25 yards from goal and Pack curled over a superb free-kick which came back off the crossbar.
Cheltenham were dominating and Luke Summerfield was not too far away with two quickfire efforts. Oxford, who had struggled to create anything in the second half, saw Peter Leven send a free-kick just wide from the edge of the area. That sparked a late flurry from the U's, but Liam Davis was wayward with a shot from distance in injury time.
The result keeps Cheltenham in sixth, with Chris Wilder's men still three points behind in the final play-off spot.
Any reproduction, publication or redistribution of this material without the written agreement of 365 Media Group is strictly forbidden.