South African Stiaan van Zyl top scored with 96 as the hosts made 292 for 6 before dismissing Glamorgan for 221 to seal victory by 60 runs under Duckworth-Lewis.
On a slow pitch, Sussex’s score was '‹boosted by David Wiese’s cameo of 35 from 20 balls at the end after van Zyl and Ben Brown (60) had laid the foundations with 115 in 17 overs for the fifth wicket.
Skipper Jacques Rudolph, on the ground where he compiled his List A best 169 not out in 2014, made his third score of over 50 in this season’s competition and all the time he was at the crease Glamorgan had a chance.
But apart from the stand of 72 in 15 overs for the fourth wicket the South African left-hander shared with Kiran Carlson, Glamorgan struggled to build partnerships and they were kept in check by some accurate bowling, particularly from Jofra Archer and left-arm spinner Danny Briggs, who finished with 3 for 53. West Indies international Jerome Taylor also picked up a wicket on his Sussex debut.
Glamorgan were 138 for 6 when rain forced the players off and after a 50-minute delay they needed a'‹n improbable'‹ 143 in 11.5 overs under Duckworth-Lewis. Chris Cooke, one of seven South Africans playing in the match, smashed three sixes in his 62 from 46 balls but an asking rate of nearly 12 runs an over proved too much.
While van Zyl played the major hand for Sussex, there were solid contributions all the way down the order as they enjoyed the best batting conditions after winning the toss.
Chris Nash scored 41 and Harry Finch 39 but it was the stand between van Zyl and Brown which really took the game away from Glamorgan.
The pair targeted the short pavilion-side boundary, particularly against Glamorgan’s seamers, with Brown hitting his runs off 53 balls with seven fours and an outrageous six over cover off Marchant de Lange.
Van Zyl scored at an even tempo throughout and looked on course for his first hundred for the county after moving into the 90s by striking David Lloyd over long on '‹for his second six having earlier driven a length delivery from Mick Hogan back over his head.
Van Zyl also hit nine fours from 88 balls faced but perished when he mis-timed an attempted pull after de Lange dropped short. De Lange had earlier bowled Brown and Laurie Evans with successive deliveries as they made room to hit through the off side. He finished with 3 for 51 and was the pick of the Glamorgan attack.
Wiese clobbered three sixes at the end and Sussex’s total always looked 30 or 40 runs above par.
Stiaan van Zyl said: "It was a great win for us and hopefully will give us some momentum for the rest of the competition.
"I thought we played well. My plan was to try and bat through because I know we’ve got some guys in the last few overs who can smash it.
"From a personal point of view it was nice to get a score. It takes time to adjust to English pitches but I felt good and Ben Brown was a great partner at the other end. His natural game is to bat with freedom and to keep the board ticking. It took the pressure off me and gave us a platform to go big at the end.
"I thought we bowled and fielded well too. They have got some dangerous players but even after the rain delay, when it can sometimes be difficult, we were professional."