City were grateful to be on level terms at the interval but then hit all three goals in the second half to deny lowly Leatherhead their first Ryman League Division 1 double of the season.
It was the Tanners who made the early running, and City had a let-off in the sixth minute when Burton shot wide from close range with only Alan Foster to beat.
The visitors were unlucky not to get a penalty when Michael Thorp appeared to trip McKay, while at the other end, Nigel Emsden latched on to a perfect through ball from Mark Druce, only for keeper Vaughan to parry his rising drive.
With Danny Wise ploughing a lone furrow up front, City were not creating anything, but it was a different story after the break.
City at last opened up the visitors in the 54th minute, Jermaine Ferreira running from halfway to turn in an excellent low cross from Emsden at the far post.
Druce dispossessed Vaughan only to shoot wide of a vacant goal, but in the 57th minute Andy Smith sent Wise through the middle and he ran 40 yards to shoot under Vaughan for No 2.
With the pressure off, City pushed men forward in search of more goals, and Wise headed into Vaughan's hands after an excellent run and cross from Ferreira.
With three minutes left, and after the visitors goal had survived a number of close shaves, Richard Peirson notched the best goal of the game when he met a perfect free kick from Matty Whitehead to head powerfully past Vaughan from ten yards.
Oxford C: Foster, Smith (Waterhouse 88), Dark, Peirson, Thorp, Emsden (Strong 68), Ferreira, Whitehead, Druce, Wise, Wimble. Sub not used: Lewis. Referee: A Laver. Attendance: 114.
City Reserves won 2-0 at Walton & Horsham Res in the Suburban League, with both goals coming from John McMahon.
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