Sussex 221 (Haines 86, Patterson 4-26) and 136 for 6 (Bess 5-33) need another 99 runs to beat Yorkshire 150 (Garton 3-25) and 305 (Ballance 74, Lyth 66, Carson 5-85)
Yorkshire took just 70 minutes to take the four remaining Sussex wickets and complete their second successive LV= Insurance County Championship win of the season at the 1st Central County Ground in Hove.
England offspinner Dom Bess took the final wicket to finish with figures of 6 for 53 as Yorkshire won by 48 runs. They collected 19 points against Sussex's four. It was always an unlikely run chase for Sussex but they - and in particular their captain Ben Brown - made a fight of it.
"It was a fantastic win, particularly from where we were on the first day," Andrew Gale, Yorkshire's first team coach, said. "We didn't do ourselves justice in the first innings but we showed great character and resilience after that. We won by a decent margin in the end and I'm really proud of them.
"The batting is an issue at the moment but to still be winning games is very pleasing. But we have got to start to put big first-innings scores on the board."
Sussex started the fourth day on 136 for 6, requiring a further 99 runs for victory, with Brown unbeaten on 26 and new batsman Ollie Robinson yet to face a ball following George Garton's dismissal from the final delivery of the previous day.
Yorkshire opened up with Steven Patterson from the Cromwell Road End and Bess from the Sea End, and with the second ball of the 59th over - the seventh of the morning - they broke through with the wicket of Robinson. The batsman pushed forward to a delivery from Patterson which nipped back and caught him in front of his off stump. Robinson's 17-ball stay had yielded just six runs.
Yorkshire knew they were through to the Sussex tail but Brown and Jack Carson, the offspinner who impressed with a five-for in Yorkshire's second innings, defied them with a stand of 35. Carson got a thick edge for four off Patterson and repeated the trick when the bowler was replaced by Jordan Thompson.
Brown, meanwhile, provided the best stroke of the morning when he drove a full-length delivery from Thompson through the covers for four.
But the intervention of England Test captain Joe Root with the ball ended the eighth-wicket stand just when Sussex hopes were beginning to rise again. Root replaced Bess and with his third delivery he made the second breakthrough of the morning as Carson edged to Adam Lyth at first slip for 18, leaving Sussex 180 for 8 and still 55 shy of victory.
Sussex lost their ninth in the next over when Thompson plucked out Brown's middle stump. The Sussex captain had batted for two hours and 21 minutes and faced 111 balls for his 46.
And it was all over in the next over when Bess, who had just been hit over mid-on for four by Henry Crocombe, had the batsman caught by the leaping David Willey at short midwicket.
"It was disappointing to lose but we played some good cricket and came out of this game with a lot of pride," Brown said. "We were up against a seriously good Yorkshire side with a number of international players and for our young team it was nip and tuck all the way.
"Tom Haines looked good again and Jack Carson went toe to toe with the England offspinner Dom Bess. We could have got more runs in the first innings but a few things didn't go our way."