Opener Chris Nash batted through with an unbeaten 56 as Sussex kept their Twenty20 Cup hopes alive with a local derby win over Hampshire at Hove.
A third Sussex defeat in four games would have made it hard to qualify.
But the home attack did well to limit Hampshire to just 122-7, of which Michael Carberry made a steady 36.
Sussex then cantered to victory on 128-2 with 17 balls to spare, Nash being well supported by Dwayne Smith (31no) and Luke Wright (28).
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