Wes Thomas put Cheltenham in front in the 25th minute with a fine strike into the roof of the net but Tom Craddock levelled in the 33rd minute, heading a Damian Batt cross into the bottom corner.
Thomas had a golden opportunity to clinch all three points for the visitors, but Clarke got down well to save his 80th minute penalty following Anthony Tonkin's foul on Brian Smikle.
Yates said: "People say we need to address our home form, which we do, but the boys have been magnificent away.
"We showed quality, tremendous workrate and great defensive nous at times.
"Wes Thomas up front was outstanding, and so was our defence. I'm slightly disappointed we didn't nick it at the end with the penalty, but Oxford are a good side."
Source: PA
Source: PA