Two lapses of concentration midway through the first half cost City dearly away to big-spending Carshalton, the 9-4 favourites for the Ryman League Division 1 title.
An excellent game with three of the goals right out of the top drawer saw City fight back strongly from a two-goal deficit early in the second period, and it was the home team who were hanging on at the end.
Excellent saves by Stuart Nelson from Hines and former Reading player Glasgow denied the hosts early on, and City shocked Athletic in the 12th minute.
Mark Druce collected a knock-down from Stuart Riddle and turned to bend his shot from the edge of the area high into the far corner.
It was 1-1 in the 22nd minute, City gifting the ball to Hegley, who crossed for McKenzie to score.
And the visitors then stood and watched Glasgow collect a throw in and cross for Hegley to notch No 2 two minutes later.
City were struggling to contain an impressive home attack, but as they gradually recovered, Druce seeing a good strike tipped over by Searle.
Athletic increased their lead in the 51st minute, former Oxford United player, Stuart Massey unleashing a tremendous shot from 30 yards which went in off the crossbar.
City were back in it six minutes later when John Mitchell raced away, and his first-time cross was brilliantly put away from an acute angle by Riddle on the volley.
Although a chip from Massey struck City's bar, it was the visitors' one-touch football that was now calling the tune, and Druce saw a low shot saved.
With two minutes left, Mitchell looked to be pushed as he headed over after a fine run by Jermaine Ferreira, but City's appeals fell on deaf ears.
Oxford C: Nelson, Farley, Dark, Gray (Mitchell 45), Thorp, Organ, Lewis, Whitehead (Ferreira 58), Druce, Riddle, Wimble. Sub not used: Waterhouse.
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