Chasing 151 for victory, English side Yorkshire completed the task with three balls to spare at the New Wanderers Stadium.
David Miller (39 not out) and Adil Rashid (36 not out) were the top scorers for the winners.
Opener Phil Jaques gave the chase right impetus after the early departure of skipper Andre Gale and Joe Root.
But after racing his way to 32 off 21 balls, Jaques offered a return catch to Dilshan Munaweera.
Miller, who came back after retiring hurt, along with Rashid, then finished the job for Yorkshire, giving them hope of qualifying for the main tournament that kicks off on Saturday.
Miller struck four fours and a six during his 29-ball knock while Rashid found the fence two times and cleared it once during his 30-ball innings.
Opting to bat, a disciplined bowling effort earlier helped Yorkshire restrict Uva Next to 150 for seven.
Steven Patterson and Moin Ashraf picked up two wickets apiece while there was one each for Ryan Sidebottom, Azeem Rafiq and Rashid.
Thilina Kandamby top-scored for Uva with an unbeaten 29 even as his other batters failed to convert the starts into big scores. MORE
