The home side had to work unexpectedly hard for their success as the visitors - including two former Tykes - showed some dogged resistance.
Sussex began the third day on 41 for 6, requiring 84 to make Yorkshire bat again and Paul Jarvis and Justin Bates shared in a seventh-wicket stand worth 36, the best of the innings.
Bates was eventually lbw to Paul Hutchison, who was awarded his second team cap out in the middle to mark that breakthrough.
Craig White then had Amer Khan caught at mid-on from a mistimed pull while Jarvis's innings ended at 51, his fourth Championship half-century of the season, when he aimed a big hit at White, missed and was lbw.
His runs came from 70 balls and included eight fours. He needed one piece of good fortune for, on 19, he was missed in the gully off Silverwood.
Even at the end Yorkshire's frustrations continued as Mark Robinson, one of the game's most notorious rabbits, contributed 18 lifting Sussex to 137.
Although Yorkshire's target of 13 was no more than a formality they lost Anthony McGrath in the first over when he was caught behind off Alex Edwards.
The Worcestershire pair, Graeme Hick and Richard Illingworth, struck centuries against Warwickshire to put their side in a commanding position at Edgbaston.
After starting his innings as nightwatchman on Wednesday Illingworth went on to score 112 before being trapped by Ashley Giles, who also claimed the wicket of Hick (122).
Kent's Graham Cowdrey and Mark Ealham scored resilient centuries against Somerset at Taunton while Derbyshire's Kim Barnett and Adrian Rollins also reached three figures to help their side recover from losing a wicket in the first over of the morning at Grace Road.
After James Ormond snapped up the wicket of Chris Adams, Barnett and Rollins took control.Reuse content