Bowlers lift Hampshire
Chasing 269 to win, a fifth wicket stand of 125 in 17.3 overs between Chris Nash (69) and Ben Brown gave Sussex hope after they had been 109 for four from 29 of their 50 overs.
But Brown, who made 62, was superbly caught by wicketkeeper Lewis McManus diving to his right midway through the 47th over.
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Hide AdThe 48th over began with 31 needed but Brad Wheal conceded just three runs from it and Sussex’s race was run when Chris Jordan, who had just driven the second ball of the 49th over for six over extra cover, was bowled off the next delivery by Ryan McLaren.
Sussex required 17 from the final over but Wheal restricted them to seven runs as they finished on 259 for six with Nash undefeated on 68.
Hampshire had earlier been indebted to a stylish 92 from opener Jimmy Adams and some late-order hitting by South African all-rounder Ryan McLaren who scored 46 off 39 balls.