The Robins won the game with a goal in each half, although they were made to hang on after Oxford's Lee Mansell set up a tense finish with a strike seven minutes from time.
Cheltenham made a dream start when on-loan striker Steven Gillespie opened the scoring from a tight angle after Kayode Odejayi had set him up with a flick header from a Craig Armstrong cross.
That goal came with only 90 seconds on the clock and within three minutes the score could have been doubled. This time Gillespie turned provider for Brian Wilson but the midfielder struck his shot straight at the goalkeeper.
After a shaky start the visitors went on to enjoy plenty of possession but the closest they came to scoring was a Neville Roach header that brushed against the outside of a post.
At the other end, Oxford goalkeeper Chris Tardif fell upon a left-foot shot from Grant McCann and Wilson hit the outside of Tardif's right-hand post with a header from a cross by Gillespie.
The second Cheltenham goal arrived right on the hour mark when Odejayi was fouled 30 yards from goal and JJ Melligan delivered a curling free-kick into the area. Defender Shane Duff, who hails from Carterton just over the border in Oxfordshire, rose highest to head past Tardif.
Substitute Damian Spencer should have wrapped the game up 13 minutes from time when he screwed a shot wide after Tardif had only parried a blast from Wilson - and the Robins were almost made to pay for that miss.
Mansell, an Oxford player but born in Gloucester, touched in at close range from a Chris Hackett free-kick to set up a tense finish that the home side just about saw out.