Opener Simon Hole steered Oxford to a six-wicket win at Radlett in the second round.
Chasing the Hertfordshire side's 204 all out, Hole hit an unbeaten 73 to take Oxford to 205-4 with four overs to spare.
He was supported by Shami Mendis with 69.
Earlier, David Taylor, the former Henley and Banbury star, who is now playing for Undercliffe in the Bradford League on Saturdays, made 50 for Radlett, while David Slade took 4-21.
Now Oxford are at home to Enfield in the last 32 on Sunday, June 25.
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