Captained by Richard Pyrah in the absence of the rested Andrew Gale, Yorkshire's young side gave a good account of themselves but Glamorgan's batsmen always had a 216 target well within their sights.
They were in some trouble when openers Gareth Rees and Mark Wallace departed to the new-ball pairing of Iain Wardlaw and Moin Ashraf, but Chris Cooke led the revival with a brisk 84 from 78 balls.
Also in Group C, acting Middlesex captain Eoin Morgan warmed up for England's limited-overs series against Australia with a season's best 90 to inspire a four-wicket win over Leicestershire at Lord's.
Although neither side could progress, Morgan caught the eye of England selector Geoff Miller - watching from the media centre - by hitting eight fours and four sixes as the hosts reached their target with 10 balls to spare.
Jos Buttler's intelligent innings of 68 not out guided Somerset into the last four with a 13-run victory over arch rivals Gloucestershire at the County Ground.
Buttler reined himself back on a two-paced pitch as wickets fell around him before the visitors posted 259 for nine after losing the toss.
Marcus Trescothick contributed 50 and Craig Kieswetter 42, but the highlight of the innings was a hat-trick from left-arm spinner Tom Smith (three for 46).
Gloucestershire replied with 246 for seven.
England Lion Michael Carberry starred with the ball as Hampshire booked a home semi-final by beating Derbyshire by 41 runs in the Group B match at Derby.
Carberry took three for 37 with his occasional off-breaks to send Derbyshire crashing to 178 all out in the 36th over in reply to Hampshire's 219 for seven which was built around 64 runs from skipper Jimmy Adams.
Chesney Hughes put Derbyshire on track with 74 off 80 balls but his dismissal sparked a collapse which saw the home side lose eight wickets for 56 in 13 overs.
Lancashire and Essex both failed to reach the semi-finals after the visitors won a high-scoring contest by 70 runs at Emirates Old Trafford.
A superb 130 for England limited-overs batsman Ravi Bopara underpinned the Eagles' imposing 297 for four, which the Lightning responded to with 227 all out inside 37 overs.
Tom Smith hit an excellent 84-ball 97 but the home side's task was too stiff. Tim Phillips nipped in with five for 42 from 7.4 overs as Lancashire lost their last eight wickets for 41 runs, slipping from 186 for two.
Also in Group B, an extraordinary onslaught by Will Smith propelled Durham to a 133-run victory over Surrey at Chester-le-Street.
The home team were struggling on 112 for five in the 23rd over, but Smith's unbeaten 79-ball knock of 120 took them to 275 for five - in partnership with Gordon Muchall (52no) - before the visitors were dismissed for 142 in 30.5 overs.
Alex Hales hit a match-winning 74 as Nottinghamshire overcame Kent by five wickets at Canterbury to top Group A and secure a home semi-final.
Hales and Samit Patel, who scored 59, put together the decisive partnership of 107 in 22 overs as the visitors overhauled Kent's 40-over total of 195 for six with 10 balls to spare.
Also in Group A, David Willey carried on where he left off in the Friends Life t20 final by pummelling his maiden senior century for Northamptonshire in their crushing 125-run win over Warwickshire at Edgbaston.
Willey made his maiden Twenty20 half-century and took a hat-trick in Northamptonshire's triumph over Surrey at Edgbaston nine days ago and enjoyed himself on his return to the ground with 10 sixes in his 101-ball 167.
Sussex finished with a flourish as Luke Wright and Matt Machan sealed a seven-wicket triumph over Worcestershire with 11.3 overs to spare at New Road.
The Royals' total of 243 for six proved to be well short of being a testing target as Sussex's second-wicket pair ripped the bowling to shreds, putting on 184 in 19 overs before falling in the space of eight balls from Moeen Ali.
Wright had plundered two sixes and 14 fours when he was caught at long on after making 112 from 69 balls and Machan was bowled for 79 after hitting 12 fours and a six from 57 deliveries.