Mark Robinson’s side showed their Division 1 pedigree to see off a promoted Hampshire side at the Ageas Bowl.
The home side, chasing 378 to win the opening clash of the campaign, were bowled out for 285 before lunch on the final day.
Sussex had it pretty much all their own way on day four after their hosts started the morning on 181-4.
An unbeaten 144 from Ben Brown combined with Luke Wright’s 96 gave Sussex a first innings total of 444.
Hampshire replied with 231 in 50 overs as Sussex new boys Ajmal Shahzad (3-54) and Tymal Mills (2-28) were amongst the wickets.
Sussex made just 164 in their second innings after Ed Joyce opted not to in force the follow-on.
Hampshire made good in roads on the third day as Michael Carberry hit 79 from 86 balls to leave them need 197 to win on the final day with six wickets in hand.
But it was a good final day with the ball for Sussex as seamer Matthew Hobden took care of Will Smith and Adam Wheater early on.
Hampshire then added just 94 for their last four wickets as Shahzad finished with figures of 3-63 in the second innings.