With Harry Gurney taking four for 22 and Darren Pattinson three for 27, the Outlaws required just 124 for victory, which was never seriously in doubt after James Taylor - who made an unbeaten 41 off 57 balls - and Samit Patel had seized the initiative with a third-wicket stand of 57 in 14 overs.
Having elected to bat on the same pitch as the one that yielded over 900 runs for the loss of 12 wickets in the County Championship, Group B leaders Surrey slumped to eight for five before recovering to make 123, their lowest total in one-day cricket for seven years.
Also in Group B, Craig Kieswetter's 47-ball half-century was enough to guide Somerset to their first CB40 win of the season, a 60-run success over Scotland at Taunton.
The England one-day wicketkeeper hit eight fours and a six in his 56 to help the hosts to 206 all out after winning the toss, Jos Buttler making 32. Jean Symes claimed three for 31 and Josh Davey three for 22.
In reply Scotland were soon 31 for four as Alfonso Thomas and Jamie Overton grabbed two wickets each with the new ball. They were eventually bowled out for 146, Richie Berrington top-scoring with 40 and Craig Meschede taking four for 27.
In the day's other Group B match, Simon Katich guided Hampshire to a comfortable four-wicket win over Durham at the Ageas Bowl with a perfectly-judged half century.
Katich struck three sixes and a four in his 59 not out as Hampshire got home with 10 balls to spare. Durham, put in on a slow wicket, managed 200 for seven from their 40 overs and Hampshire reached 201 for six as Kabir Ali gleaned the winning single off Mitchell Claydon. Gordon Muchall had earlier underpinned Durham's total with a defiant 96 not out.
In Group C, Australia's Usman Khawaja scored his maiden one-day century for Derbyshire as they recorded a double over the Unicorns with a 35-run victory at Chesterfield. Khawaja made 104 from 109 balls and shared a century opening stand with Chesney Hughes who made 66 out of the Falcons' 235 for seven.
Luis Reece led the chase with 59 from 63 balls but his dismissal in the 35th over ended the Unicorns' slim hopes and they were bowled out for 200, with Mark Turner taking four for 54.
Elsewhere, the matches between Middlesex and Leicestershire and Gloucestershire and Essex were both abandoned without a ball bowled due to wet outfields.