The home side were bowled out in 40.2 overs for just 216 after winning the toss, George Bartlett top-scoring with 40, while Roelof van der Merwe contributed 38. Kyle Abbott was the most successful bowler with three for 36.
In reply, Hampshire cruised to their seventh victory in eight group matches with more than 18 overs to spare, Aiden Markram leading the way with 61, Aneurin Donald making 57 and Sam Northeast 51 not out.
It was Somerset’s third successive defeat in the competition. After winning their first four games, they now face a battle to qualify from the group.
Liam Dawson, Gareth Berg and Mason Crane also did plenty of damage for Hampshire.
When Lewis Gregory edged Fidel Edwards through to wicketkeeper Tom Alsop Hampshire were in total control.
Somerset managed to rally a bit from 141 for six but the visitors still kept in total charge.
Hampshire’s innings was given an early boost by Donald, who hit two sixes from successive balls in the fifth over, bowled by Josh Davey.
Tom Alsop soon joined in, hitting Davey for three fours and a six in his next over before pulling a catch to short fine-leg off Craig Overton to make it 49 for one in the eighth over.
Markram deposited a short ball from Gregory over fine-leg for six and then swung Jamie Overton, having his first bowl of the season following injury, to a similar area for four.
Donald eased to a half-century off 50 balls, with five fours and two sixes, but was out with the total on 113.
By then Makram was set and he followed Donald to a fluent 50, with six fours and two sixes, before being caught and bowled by Craig Overton, parrying the ball above his head and catching it as it came down.
It was far too little too late for Somerset as Northeast and Rilee Rossouw saw Hampshire home, the latter hitting a big six over mid-wicket off Jamie Overton and Northeast reaching a 56-ball half-century with a six off Davey to end the game.