Tasmania 309 for 7 (Silk 94*, Ward 64) against New South Wales
Third-placed NSW entered the match knowing they needed to win to have any hope of reaching the final, which will be hosted by South Australia.
The strong first-innings total by Tasmania means NSW have plenty of work ahead of them to get a positive result.
Tasmania slipped to 44 for 2 after Jake Weatherald (nine) was caught a slip and Nivethan Radhakrishnan (10) was trapped lbw by Ben Dwarshuis.
But a 65-run stand between Ward and Jewell, followed by a 82-run stand between Ward and Silk put Tasmania into a strong position.
Silk has the chance to post his 12th first-class century when play resumes on Sunday.
Tasmania sit in last spot on the table and are no hope of reaching the final.
But it’s all on the line for NSW, who must beat Tasmania and then rely on second-placed Queensland failing to get a win against ladder leaders South Australia.
The match also represents another opportunity for NSW opener Sam Konstas to put his name up in lights ahead of Australia’s Test Championship final against South Africa at Lord’s in June.
Konstas made a stunning Test debut against India in the Boxing Day Test, but his topsy-turvy form of late has been a big talking point.
The 19-year-old rebounded with an important half-century in last week’s Shield draw with WA at the WACA, and his performance against Tasmania will be highly scrutinised as Australia’s selectors mull over who should partner Usman Khawaja at the top of the order.