Hampshire 227 for 6 (Rossouw 90, Weatherley 46*, Clarke 4-48) beat Surrey 262 for 7 (Elgar 91, Borthwick 46*, Crane 3-45) by four wickets (DLS method)
Legspinner Crane grabbed 3 for 45 on his first appearance at the Ageas Bowl since making his Test debut over the winter, before Rossouw blasted a memorable 90, and Joe Weatherley bundled Hampshire over the line, to condemn Surrey to their second defeat of the tournament.
Hampshire were set 227 to win from 34 overs, on DLS method, after Surrey had amassed 262 in 44 rain-affected overs, thanks to Dean Elgar's 91.
Rossouw and Hashim Amla set about the task enthusiastically, with the latter creaming a series of cut shots to the boundary. But the former South Africa Test captain, having helped put on 52 for the first wicket, was leg before to a Rikki Clarke ball that jagged in.
Rossouw then went on the attack, plunging Sam Curran and Clarke for sixes on the way to a 34-ball fifty. Vince scored 14 in a 63-run partnership with Rossouw before he was bowled by Gareth Batty while attempting to give himself space to drive.
Weatherley joined the swashbuckling Rossouw to add the third half-century stand of the innings but Rossouw fell ten runs short of what would have been a deserved ton as he was bowled by Clarke.
Jimmy Adams and Brad Taylor both came and went, skying to Foakes and Meaker respectively, before Gareth Berg, who had received a reprieve as replays showed his edge behind hadn't carried, was bowled - all three to Clarke.
Curran spilled Lewis McManus at third man before the wicketkeeper-batsman, along with Weatherley, 46 not out, edged Hampshire to victory with seven balls to spare.
Earlier, Rory Burns won the toss and elected to bat on a good-looking wicket, which was to offer equal assistance for bat and ball, with both sides deciding to pick unchanged XIs from their opening matches.
England Under-19s star Will Jacks drove to a diving Jimmy Adams at short cover in the sixth over to bring Burns and Elgar together to add 93 for the second wicket.
Elgar produced a scrappy innings, full of swings across the line and dabs into gaps, but while it wouldn't win any style points it proved effective.
The South African reached his half-century from 50 balls before spinners Crane and Brad Taylor started the mid-innings squeeze. Crane struck in three successive overs to have Burns, for a well-made 46, and Ollie Pope lbw before producing a devilish delivery to beat Ben Foakes outside his off-stump, with Lewis McManus completing the stumping.
While Crane was making the headline by taking wickets, Taylor was stopping the runs - their combined statistics a miserly 3 for 88 from 18 overs.
The fast bowlers returned and Fidel Edwards delivered a rising bouncer which bruised Curran's glove before being caught behind. And then Berg had Elgar chopping on for 91, before the rain paused the game after 37.1 overs - eventually play resumed with the match cut to 44 overs a side.
From the remaining 6.5 overs, Surrey managed to score 64 runs, with Scott Borthwick and Clarke putting on 56, with the latter lbw to Edwards in the penultimate over but it wasn't enough to prevent Rossouw's fireworks.