Captain James Vince struck 81 as the Ageas Bowl side registered a first-innings score of 188 for three.
Meanwhile, Kyle Abbott shone with the ball and finished with figures of three for 22.
Despite Hampshire beating Glamorgan last Friday, the South African struggled in his four overs in Cardiff.
Abbott admitted he worked with his coaches to improve after his performance in south Wales.
He is now challenging himself to be his side’s talisman with the ball.
Abbott said: ‘We have come into the competition with a bit of energy and we have won two tight games and got some momentum going.
‘We had a great partnership up front between Rilee Rossouw and James Vince and, hopefully, they can kick on during the season.
‘On Friday, in my final over I bowled I went for 11 runs.
‘I did a bit of work with the coaches and tonight was much better.
‘I want to bowl during key overs and take wickets, as well as challenge myself at those important stages of an innings.’
Vince and Rossouw (46) gave the visitors a superb start and shared a first-wicket partnership of 109.
The Hampshire captain and Michael Carberry (41 not out) continued to pile on the runs and the Ageas Bowl side ended on 188 for three from 20 overs.
Sussex began well and a half-century from Luke Wright made things competitive.
However, tight bowling from Abbott, Mason Crane (two for 24) and Gareth Berg (two for 44) meant Sussex finished on 169 for seven.
Vince & Co host Middlesex in the T20 Blast at the Ageas Bowl tomorrow (7pm).