Sussex managed to total 251 largely thanks to an aggressive fifth wicket stand of 115 in 24 overs between Luke Wright, who hit a six and 10 fours in 59 from 77 balls, and Chris Nash, whose 76-ball 48 with nine fours was his best score of a so far poor summer with the bat.
Hampshire hit back well with the ball, though, and then replied with 116-4 in 34 overs as Vince led the way with a 61-ball half-century that included nine fours.
South African-born former Middlesex seamer Berg took 3-24 in the morning session to check Sussex from 47 without loss to 87-4, and later picked up a further wicket as the home team slumped from 202-4 following the Wright-Nash counter-attack.
Berg’s scalps were all the result of sharp catches in the slip cordon, with Vince pulling off a particularly brilliant diving effort high to his right at second slip to remove Ed Joyce for nine.
Vince was also the catcher when Berg struck in his first over to dismiss Luke Wells for 16 and his other victim in the pre-lunch session, after Sussex had chosen to bat first, was Mike Yardy – who nibbled to third slip after reaching a punchy 41 off 54 balls.
Hampshire, bottom of the first division and the only county yet to record a championship victory this season, were then guilty of bowling too short too often as Wright and Nash, who had already rallied their side by adding 38 in 8.3 overs immediately before lunch, continued to go for their shots in the early afternoon sunshine.
Jackson Bird, the Australian fast bowler, marked his first championship appearance as Hampshire’s overseas player by pinning Matt Machan leg-before for 13 in mid-morning with one that kept a little low on a lively pitch that, more often than not, offered bounce as well as seam movement from a slightly-cracked surface.
Bird, though, was punished heavily by Wright and Nash, who pulled and cut anything short with relish, and it was with some desperation that Hampshire captain Jimmy Adams called up Vince to bowl his occasional seamers in the 45th over.
Wright pulled him unceremoniously for six but, from the last ball of Vince’s first over, Nash swung another long hop straight into the hands of deep square leg and hung his head in horror and disbelief at what he had done.
Then, to the very next ball at the start of the following over, Wright fell to slow left-arm spinner Danny Briggs, who made one spit up from just short of a length to take the edge of the bat and loop to slip.
Ollie Robinson, Ben Brown and Fynn Hudson-Prentice, a 19-year-old all-rounder from Haywards Heath making his first-class debut due to the injury crisis which has sidelined four Sussex quicker bowlers, were all dismissed cheaply as Hampshire worked their way through the lower order.
Robinson (6) was caught at first slip to give Berg his fourth wicket, Brown (7) edged Fidel Edwards also to Sean Ervine at first slip, and Hudson-Prentice (15) spliced an attempted pull at Bird to mid-on.
Vince claimed his third catch at second slip when Steve Magoffin, on 11, flashed at Bird to become the last Sussex wicket to fall. That gave Bird final figures of 3-69.
Hampshire’s reply got off to an unfortunate start when Adams, backing up, was run out when Magoffin deflected a fierce straight drive by Sean Terry into the bowler’s stumps.
Terry, dropped at second slip off Matt Hobden on 20, played some fine strokes to get to 30 from 44 balls before he edged Robinson’s fast-medium to Nash at third slip and Michael Carberry, who had pulled Robinson for six and square driven him for four in an over costing 15, edged behind a beauty from the returning Magoffin to go for 14.
Vince batted with positive intent in the final hour to keep Hampshire’s score moving forward but he lost Will Smith at 99 when Robinson had him lbw for seven playing across the line.
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