Gary Ballance and Ryan Sidebottom put on an eighth-wicket stand of 81 to hold Sussex at bay and unexpectedly allowed Yorkshire's LV= County Championship to go into a fourth and final day.
Sidebottom departed after resisting for 29 overs and when bad light ended play shortly afterwards Yorkshire were 228-8 and still requiring a further 32 to force the visitors bat again.
Left-handers Adam Lyth and Phil Jaques gave the home side hopes of a batting revival when play finally got underway following a murky morning, the Australian cutting Steve Magoffin hard for four and Lyth boosting his confidence with consecutive boundaries off James Anyon.
After a second wicket stand worth 56 Lyth flicked a leg-side ball from Anyon into Ben Brown's gloves, Andrew Gale steered his second shot against Anyon to captain Ed Joyce at third slip.
Another useful stand developed between Jaques and Jonny Bairstow, who pulled and cut Anyon for boundaries, and the England man also drove Chris Jordan through mid-off for four.
Magoffin dealt a massive blow to Yorkshire by sending down a fine delivery which Jaques had to play at and he only succeeded in edging a slip catch to Mike Yardy, his 57 coming off 99 balls.
The paceman struck again with his next ball which Azeem Rafiq played into his stumps and although Liam Plunkett survived the hat-trick ball he, too, fell to Magoffin soon after tea when he played down the wrong line and was bowled.
At 140-7 Yorkshire were in deep trouble but Ballance showed plenty of spirit and was ably supported by Sidebottom who loosened Monty Panesar's tight grip by swinging him over mid-wicket for six after Ballance had swept the left-arm spinner for four earlier in the over.
Sidebottom even faced most of the bowling and each batsman had received 109 deliveries when Sidebottom departed to his next ball, caught by Jordan at first slip off Anyon for 48 with four fours and a six.
The light deteriorated rapidly again and the players came off at 228-8 with nine overs remaining, leaving Ballance unbeaten on 46 from 113 balls with five boundaries.