Hampshire 308 (Dawson 115, Brook 5-56) and 330 for 3 dec (Gubbins 139*, Vince 63, Middleton 52) beat Somerset 137 (Barker 5-32) and 316 (Kohler-Cadmore 84, Dawson 4-85) by 185 runs
Tom Kohler-Cadmore scored a well-made 84, but Hampshire's patience was rewarded with their sixth LV=Insurance County Championship victory of the season.
Kohler-Cadmore and James Rew's 107-run stand threatened to frustrate odds-on-favourites Hampshire, who had taken two early wickets. But Liam Dawson plugged away with 4 for 85 before the second new ball opened the visitors up as Hampshire won by 185 runs before tea, with 33 overs shy of survival.
Hampshire, whose title ambitions were ended by Surrey's victory the previous day, took 21 points to Somerset's three - with both sides only battling for prize money in the final month of the season.
Hampshire needed eight wickets, Somerset a less likely 400 runs on the final day at the Ageas Bowl. Somerset were rolled for 137 in the first innings, and when Sean Dickson - who had completed a half-century the previous evening - was castled by Mohammad Abbas to the 11th ball of the day, it felt like a landslide victory was coming for the hosts.
Andy Umeed, who had played his part in the 68-run stand with Dickson, edged a rising Abbas delivery to second slip two overs later to make the lunch orders start to feel redundant. But Kohler-Cadmore and Rew bedded in and ate away at the overs.
Kohler-Cadmore was skittish and refused to err from his aggressive tendencies, with plenty of plays and misses in the early part of his innings exciting the Hampshire cordon.
His lack of fear might not have been the traditional way to save a match for his team, but it benefited both his side and himself - with his fourth half-century of the season coming in 67 deliveries. Rew took 16 balls to get off the mark and at various points was three of 31 and 11 off 49 but never seemed bogged down or frustrated.
The pitch remained as slow and flat as it had been across the match, with Dawson finding some significant turn, and very occasional spit out the rough, but it was much too slow to provide a stern test. However, the left-arm spinner did break the 107-run alliance between Kohler-Cadmore and Rew.
Rew had retaken his place as the highest run-scorer in Division One, he now has 1,077 runs, but a drive away from his body found an inside edge and was caught by wicketkeeper Ben Brown.
Kohler-Cadmore's resistance ended on 84 with a brilliant off-spinning delivery from Tom Prest five overs before the second new ball. It caught the edge of the rough wide of off stump to turn back and bowl the slog-sweeping batter. It was the former England under-19 captain's maiden first-class wicket.
The second new ball pulled the rug out from under Somerset's resolve. Lewis Gregory edged Kyle Abbott behind to the fourth ball with the new cherry. Neil Wagner was castled by the South African quick in his following over, before Dawson bowled Jack Brooks and had Shoaib Bashir lbw to complete the victory.