A late penalty from substitute Peter Leven brought the Us back into the match at Whaddon Road, and the hosts had to survive a nervy final 10 minutes before the points were secured.
The visitors went close to opening the scoring when Robins' goalkeeper Scott Brown had to tip Jon-Paul Pittman's long-range effort round a post.
As the first half progressed, Cheltenham gradually gained the upper hand and they eventually went ahead just before the half-hour mark. Billy Jones found the supporting Carter, who opened his Town account with a cleanly-struck left-foot shot from 25 yards.
Adam Chapman almost brought Oxford level soon after the restart, but his powerful free-kick rattled a post.
Harrad then doubled the home side's lead when he smashed a thunderbolt into the top corner to record his fifth goal of the campaign. Leven converted Oxford's 80th-minute penalty, awarded after Alan Bennett held James Constable, but Cheltenham held on despite Chapman and Deane Smalley going close from long range.