Somerset made a fast start after being put in at Taunton and were 70-1 after 38 balls as Will Smeed brought up his half-century from 29 deliveries.
When Smeed fell to Eddie Jack for 68 from 37 balls, with nine fours and three sixes, Somerset were 116-3 with more than nine overs to come, but the visitors battled back with Tom Abell, Sean Dickson and Ben Green departing for the addition of just 11 runs across 17 deliveries.
Lewis Gregory and Lewis Goldsworthy came together at 127-6 with 38 balls remaining and posted a T20 club record stand of 82 for the seventh wicket as skipper Gregory eventually departed from the final ball for 55 from 27 balls, with Goldsworthy unbeaten on 29 from 16 balls in their total of 209-7.
In reply, Lhuan-dre Pretorius and James Vince amassed 56 in the six-over powerplay but the South African was caught in the deep for 37 and Toby Albert soon followed as Hampshire were 95-2 in the 12th over.
Vince (54) brought up his half-century from 29 deliveries with a six off Green but was caught off the following ball.
Dewald Brevis and Joe Weatherley needed an unlikely 103 from 7.2 overs and the game was effectively up when Weatherley (15) was run-out by Riley Meredith, who then bowled James Fuller.
Brewis hit four sixes in a 16-ball 36 but the Hawks eventually went down by 17 runs to stay fifth.
