Hampshire last won the competition a decade ago. Batting first, Tom Purst made 64 off 46 balls for Hampshire and anchored a total of 190, before Hampshire constrained Somerset with a disciplined bowling performance.
Nathan Ellis used a subtle variation of his pace to start the rot as Will Smeed used a pull at mid-on and the Australia seamer took three for 30 by bowling Jack Brooks and Peter Siddle.
Openers Smeed and Tom Banton could not contribute much in the chase and both openers returned to the pavilion in the powerplay itself. In-farm Riley Rossouw could also score 23 runs in just 20 balls.
Captain Tom Abell contributed 27 runs but was dismissed for a deep midwicket boundary. Lewis Gregory took Somerset to three points with a straight six off his second ball, but they still needed 87 from the final 42 balls, with Hampshire firmly in pole position.
Gregory chased Rossouw and Abel to be caught in the deep on the leg-side, while Ben Green was run out in the middle of a mid-pitch mix-up with Tom Lamonby, the last recognized batsman so far.
Lamonby contributed 34, including a straight six off Fuller, but 54 was needed in the last three overs. Ellis returned for the final over and cleaned up the lower order pair of Siddle and Brooks in successive deliveries to wrap up the match.
James Vince chose to bat first and he and Ben McDermott got off to a good start against Somerset’s bowling attack.
There were some trademark drives from Vince (20 off 12) and three heves for six from McDermott (31 off 17), although the pair was also dismissed in the powerplay but after collecting 65 runs in 6 overs.
Weatherly (24) and Ross Whiteley (27) made cameos for Hampshire before Perst pulled out the shackles in the last over, first ball to slow left-hander Roulof van der Merwe (2 for 29). He was dismissed on the next ball before being dismissed.