Sussex blew their lines with the bat and suffered defeat before a big crowd at Hove.
Hampshire recorded only their second Championship win of the season when they beat the title-chasing hosts by 118 runs inside three days.
Sussex, chasing their fifth victory in eight games, required 253 for victory after bowling out Hampshire for 220 and were favourites when they reached 64 for one at lunch.
Hampshire were once again looking to veteran fast bowler Kyle Abbott to do something heroic.
But instead it was fellow fast bowler Eddie Jack who seized the day with figures of four for 36, his best return in his 13th first-class match. And he was well supported by off-spinner Felix Organ who took three wickets.
The sunny conditions favoured the batters, unlike the previous day, but the slight variable bounce in the pitch always offered encouragement to the bowlers and in challenging circumstances Sussex didn’t have a batsman capable of taking the initiative.
Hampshire had started the third day on 206 for nine, a lead of 238, with last pair Abbott and Jack having already added 33 for the tenth wicket and added another 14 runs.
Sussex started their pursuit amid great tension, with the result of crucial importance to both sides.
Every run was cheered by a large crowd who were given free admission. But there was also a large contingent of Hampshire supporters.
Hampshire broke through in the third over when Tom Haines was lbw to Abbott for a duck. But left-handers Dan Hughes and former Hampshire player Tom Alsop swung the match Sussex’s way.
Runs were hard to come by but then Hughes drove Jack for three fours in an over, through the covers, straight and through midwicket.
At lunch Sussex looked the better bet, with Hampshire hopes resting primarily on Abbott. But it was Jack, charging in from the Sea End, who swung the match towards the visiting side with two wickets in consecutive overs.
At 67 he had Hughes lbw as the batsman attempted to flick a full length delivery through midwicket, ending a partnership worth 58 runs.
Then, without addition, he had Jack Leaning caught behind for a pair, the ball just carrying to former Sussex captain Ben Brown.
At the other end Tom Alsop was playing with calm assurance. But when he had scored 37 he cut Felix Organ to backward-point where Scott Currie claimed the catch. But Alsop didn’t move and he was eventually given not out by the square-leg umpire.
It felt like a turning point but Alsop had added just six runs before he edged the same bowler to Toby Albert at first slip.
And, in the next over, the game turned sharply in Hampshire’s direction when James Coles was caught behind attempting to cut a short, wide delivery from Jack.
Jack struck again in his next over, having Tom Price caught down the leg side. And then Organ struck twice in two deliveries, having Carson caught at short-leg and Dom Goodman caught behind. At tea Sussex were 134 for eight.
Without addition, John Simpson was caught at mid-on off Abbott and Sussex lost their last wicket next ball when Jaydev Unadkat was caught in the gully first ball.
Sussex had lost their last nine wickets for 70 runs after lunch.
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