Batting first, Gloucestershire made 230 including 74 from captain Chris Taylor.
But Surrey skipper Mark Ramprakash trumped that with 84 although it needed a composed 62 not out from England all-rounder Rikki Clarke to see the 'Brown Hats' home in a tight finish.
Hampshire eased past Glamorgan at Sophia Gardens after a One-day best of 114 not out from wicket-keeper Nic Pothas and England One-day International batsman Kevin Pietersen (69 not out) shared an unbroken match-winning partnership of 130 as Shane Warne's men beat the Welsh County by six wickets.
Earlier, Zimbabwe all-rounder Sean Ervine took five for 50 as Glamorgan were bowled out for 214.
England wicket-keeper Geraint Jones scored 70 for Kent as Derbyshire were beaten by 127 runs while Warwickshire veteran Dougie Brown took three of the first four Leicestershire wickets to fall as his side triumphed by 83 runs.
Long-serving Middlesex all-rounder Paul Weekes scored a hundred but it was not enough to prevent his team losing by 19 runs against Northamptonshire at Lord's.
Northamptonshire's Australian medium-pacer Damien Wright took four for 38 from 9.3 overs including a spell of four for one in seven balls which finished the match.
Anthony McGrath made 74 as Yorkshire just did enough to hold off Worcestershire, last season's beaten finalists, by 14 runs at Headingley.
Sussex, who beat Bangladesh in their tour match on Tuesday, and Nottinghamshire complete the second round fixtures on Wednesday.
Lancashire will play the winners of that match while other last eight fixtures see Surrey at home to southern neighbours Hampshire, Warwickshire up against Kent and Yorkshire facing Northamptonshire.
The quarterfinals will take place on July 15 and 16.