Top of the table Oxford and in-form Cheltenham cancelled each other out in a game in which defences were largely on top.
The best chances either side had for a goal arrived in the first half.
Cheltenham were indebted to their goalkeeper Shane Higgs for two excellent saves in the moments leading up to half-time while at the other end, striker Kayode Odejayi was guilty of missing a couple of good chances.
It was a fast-paced but untidy first 45 minutes with both sides displaying much huff and puff but little invention.
Odejayi, who was booked early on for a foul on defender Andy Crosby, arrived onto a low cross from Kevin Amankwaah but was unable to touch it past goalkeeper Andy Woodman from close range.
Higgs performed his heroics with a flying stop from Steve Basham and instinctive reflex save from Derek Townsley, both incidents coming in quick succession, but Odejayi had a further chance to give Cheltenham the lead when he headed wide from another Amankwaah cross.
Oxford's Basham blazed high from the edge of the area after Higgs had spilled a high cross under pressure from Townsley, but it was to prove a disappointing second half.
Cheltenham pressed forward for most of the second period but were unable to prise open the visiting defence.
Grant McCann went close with a couple of free-kicks and Lee Howells, back in the team after an 18-month injury absence, tried his luck with a couple of long shots but that was about it.
The main talking point arrived in the 89th minute when Cheltenham defender Michael Duff was sent off for bringing down Oxford midfielder Dean Whitehead.
Duff was clearly unhappy with the decision and the ugly brawl that followed also resulted in a booking for Robins captain Mark Yates.