David Lloyd and Colin Ingram scored half-centuries for Glamorgan but Somerset reached the target of 181 to win by eight wickets.
Jeremy Lawlor added 43 on his T20 debut as the home side recorded 180/6 but Glamorgan fell to defeat in their opening game of the season.
"With 180 you're always in the game," said Ingram. "It was a little disappointing as we lost our way after an excellent opening stand between two young players upfront.
"My first 15 runs were probably some of the worst in my career, I felt terrible, but I changed a few things and got a few away at the end to push our total up.
"It was a good wicket and they played some inventive shots upfront, we couldn't find a way to get a wicket, and credit to them they played out of their skins."