Craig Haupt was Banbury’s hero, hitting 65 in their total of 150-7.
Banbury then restricted Oxford to 101-9 thanks to tight bowling, particularly by stand-in captain Jimmy Phillips, who took 3-15.
He was well supported by fellow spinners Luke Ryan and Jaimie Noble.
Earlier, Banbury had beaten Henley by five wickets in the semi-final of the competition, held at Bicester & North Oxford.
Phillips said: "We are really pleased. We faced two strong sides in Henley and Oxford.
"Craig Haupt batted a superbly aggressive innings. The spinners bowled really well and put the ball in the right place."
The cup victory was the culmination of a good weekend for Banbury, who beat Finchampstead in the league the previous day.
They won by seven wickets and set up an exciting finale to the season on Saturday. They face High Wycombe, who are just one point ahead of the them in the table.
A winning draw would see Banbury leapfrog them into fourth, which was the club’s target for the season. There is still a slim chance they could end up third.
Victory on Saturday came despite the absence from the batting line-up of Hector, who had broken two fingers while fielding and will miss the High Wycombe clash at Bodicote.