England off-spinner Dom Bess took the final wicket to finish with 6-53 as Yorkshire won by 48 runs.
They collected 19 points to 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.
Sussex started the day on 136-6, 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.
With the second ball of the 59th over – the seventh of the morning – Yorkshire 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.
Sussex had added just nine runs and Robinson’s 17-ball stay had yielded just six runs.
Yorkshire knew they were through to the Sussex tail but Brown and Jack Carson 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.
At the other end, at 180-7, England captain Joe Root replaced Bess and with his third delivery he made the second breakthrough of the morning when Carson edged to Adam Lyth at slip for 18.
Sussex lost their ninth wicket in the next over when Thompson plucked out Brown’s middle stump.
The Sussex captain, who appeared to be unlucky with his first innings dismissal, had batted for two hours and 21 minutes and faced 111 balls for his 46.
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.