The Grecians' triumph ended Oxford's 100% home record as the U's were brought down to earth after their midweek derby cup win over Swindon.
Cureton ran 40 yards through the middle of Oxford's backline in the 11th minute and, with defenders backing off, drove powerfully past 'keeper Ryan Clarke from 18 yards. Sixteen minutes later midfielder Scot Bennett doubled the Grecians' lead with a thumping header from Liam Sercombe's corner.
Cureton, 37 years young, showed good pace before firing in a third at the start of the second half, taking his season's tally to five goals.
Oxford threatened a comeback as Jake Forster-Caskey converted a penalty after Craig Woodman tripped Damian Batt and Alfie Potter bundled in a second. But the excellent John O'Flynn wrapped it up for City with a low angled drive.
Oxford's day then got even worse with James Constable sent off for two quickfire yellow cards nine minutes from time.