Hampshire 208 for 5 (Vince 129*, Prest 62) beat Somerset 194 for 9 (Rossouw 55, Banton 54, Wood 2-26) by 14 runs
The result left Somerset still second in the South Group table, while Hampshire moved into the top five.
Vince's amazing assault bettered the unbeaten 124 made for Hampshire by Michael Lumb in a T20 game against Essex at Southampton back in 2009.
The monumental innings was even more praiseworthy for the fact that he lost opening partner Ben McDermott to the third ball of the game, caught top-edging a pull shot off Tom Lammonby.
Somerset restricted the Hawks to 45 for one off the powerplay and would still have been happy with the situation at the halfway point of Hampshire's innings when they were 83 for one.
But by then Vince had cleared the ropes three times and Prest once. Both batsmen reached their half-centuries in the 13th over, Vince first off 36 balls quickly followed by the impressive Prest off 38.
Prest then departed, having faced 46 balls and hit two sixes and six fours, edging a wide ball from Jack Brooks through to wicketkeeper Banton.
But by then Vince was scoring so quickly it barely mattered. He reached his fourth Blast ton with two fours and a two off the first three balls of the 18th over, his second fifty having come off just 15 deliveries.
Ross Whiteley, Joe Weatherley and James Fuller fell cheaply. But when Vince launched the last ball of the innings from Peter Siddle over mid-wicket for his tenth six it completed an unforgettable innings.
Rossouw hit his first two balls for four and six as the hosts progressed to 104 by the end of the tenth over, Banton going well on 38.
Dropped on 43 by Prest at deep mid-wicket off Fuller, he moved to a 34-ball fifty with an audacious reverse sweep off Ellis, which cleared the stands.
When Wood bowled Banton behind his legs, Somerset needed 78 from 45 balls. That had been reduced to 42 off 23 when Tom Abell was caught attempting a ramp shot off Wheal.
The home side surprisingly sent in George Bartlett for his first Blast appearance of the season and he could make only two before being bowled by Wood.
Momentum was lost as Wood, Wheal and Ellis combined effectively with the ball at the death.
Rossouw moved to his sixth fifty in 11 South Group games off 25 balls. But when he went to the first ball of the 19th over, caught in the deep off a Liam Dawson full toss, Somerset's race was run and a clatter of wickets saw them fall well short.