Worcestershire 334 for 6 (Libby 109*, Kashif 73) beat Sussex 333 for 9 (Hudson-Prentice 68, Leaning 50, Gibbon 3-74) by four wickets
The impressive left-hander Isaac Mohammed and Brett D’Oliveira had put on 60 for the first wicket in 11 overs before D’Oliveira skied Jack Carson to Ollie Robinson at long-on.
Isaac was second out at 83 when he top-edged to midwicket and Sussex were on top when Rehaan Edavalath, sweeping, had his off stump knocked by Carson; 105 for 3 in the 20th.
But Libby and Kashif turned the match, targeting 19-year-old seamer Freddie Price, who conceded 20 in the 33rd over to bring up the Worcestershire 200 and the 100 partnership.
Sussex hit back with the wickets of Kashif and the gifted Henry Cullen but Libby remained to see his side home with the big-hitting Ben Allison, who struck 20 off nine balls.
At one point Sussex looked capable of reaching 350. Haines and Charlie Tear got the Sharks off to a flyer after the Rapids had won the toss and chosen to bowl, although Haines on nine was missed at first slip off Ben Allsison.
Both men drove fluently to bring up the fifty from 54 balls and at the end of the ten-over powerplay they had shared 13 boundaries in a score of 66.
Worcestershire broke through in the 11th over when Tear, who had scored a run-a-ball 30, clipped Ben Gibbon to midwicket where Isaac took a good low catch.
Four overs later, his opening partner fell, Haines playing a flat-footed drive and edging Gibbon to the keeper for a 48-ball 40.
George Thomas and Oli Carter then put on 40 for the third wicket in six overs. But not for the first time this season the Sharks were struggling to find a top-order batter capable of playing a definitive innings.
Carter had made just 22 from 24 balls when he spooned a gentle catch to mid-on. Thomas hit three fours and the first six of the day when he hit left-arm spinner Fateh Singh back over his head. But then he was yorked by the clever leg-spinner D’Oliveira for 39.
