The hosts posted an impressive 199 for six after losing the toss, Craig Kieswetter contributing a rapid 37 off 18 deliveries and Dean Cosker escaping the carnage to take two for 18 from his four overs.
Jim Allenby and Mark Wallace got Glamorgan's reply off to a smooth start with a stand of 73 in eight overs, Allenby cracking 69 off 39 balls, with seven fours and three sixes.
But once he had fallen to the leg-spin of Max Waller (four for 27) the visitors lost their momentum and plunged from 73 for one to 111 for seven with only five overs remaining before being bowled out for 135 in 18.1 overs.
The result keeps the Midlands/Wales/West Division open, with Glamorgan having won four and lost two, while Somerset have three victories and three defeats.
A stunning innings of 72 not out from Ben Stokes, his highest score in Twenty20 cricket, took Durham to a three-wicket victory over Nottinghamshire at Trent Bridge and lifted his side from the foot of the North Division.
Stokes had arrived at the crease in the sixth over with his side in some difficulty at 30 for three, in pursuit of a victory target of 160. He faced 48 deliveries and hit one four and five sixes, each of them coming from a different Outlaws bowler.
Despite Stokes' heroics, he needed the help of Michael Richardson to get Durham over the line, with the winning run being scored from the final ball of the contest. Earlier, Notts had posted 159 for seven after being invited to bat first, with James Taylor contributing a measured 54.
Unbeaten Hampshire returned to the top of the South Division following a comfortable seven-wicket victory over Surrey at the Oval.
Sean Ervine, who made a run-a-ball 28, and Liam Dawson, who finished with an unbeaten 24, added 37 in seven overs to see the Royals home with 10 deliveries to spare after Surrey could only muster 126 for six.
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- Jim Allenby