Glamorgan, who turn professional next season, won the League Two T20 Blast earlier this month and were returning to the 50-over group stage for the first time since May.
They gave Warwickshire’s Abbey Freeborn her first loan game of the season, but she was unable to repeat last year’s century at Neath as she was bowled for 14 by Buckle in the fourth over.
Lauren Parfitt and Sturge added 94 for the second wicket, Parfitt striking three fours and a six before being bowled by rival skipper Green (2-43).
But wickets fell regularly after that, Sturge hitting six boundaries in her knock off 89 balls before she was sixth out to former Glamorgan loan player Poppy Tulloch (2-47).
Porter tried to hold the lower order together with an unbeaten 34 off 35 balls, but Buckle and Johnson claimed a further two wickets apiece as Glamorgan were dismissed with five overs unused.
Sussex opener Mollie Adams hit a quick 25 before Izzy Collis (25) and Wilkinson added to a solid platform with a stand of 55 for the second wicket.
Glamorgan’s change in tactics to field two seamers, Anna-Mae Shearn and Surrey teenager Charlotte Lambert, did not quite pay off despite two wickets for Lambert.
Wilkinson struck six boundaries in her half-century before becoming the first victim for Porter as the Sharks faltered briefly at 143-5.
Green and Johnson (27) got them in striking range with a stand of 68, but Porter had Green stumped by Freeborn for the first of three victims in quick succession.
Tulloch and Buckle came together for the ninth wicket with 19 still needed, but the pair held their nerve and Buckle coolly ramped Lambert for four to seal the result.
Glamorgan remain top of the table but have only a three-point lead over Middlesex, who have a game in hand despite losing to Kent, while Sussex are third, a point further behind after claiming their third win in five.
The top four will contest the semi-finals in September with the final at Bristol.