Jewell's 102, his ninth first-class century, lifted the visitors to 2-196 at Cricket Central at stumps on day two in reply to NSW's 9-391 declared.
Tasmania's plans were disrupted by a concussion to allrounder Aidan O'Connor and a leg injury to fellow allrounder Mitch Owen on day one.
They were replaced by pace bowler Jackson Bird and batter Charlie Wakim.
The competition has this year introduced injury substitutes who can play in a game under set conditions, so Wakim will be able to bat.
Tasmania opened their batting with legspinner Matthew Kuhnemann and he performed a sterling job in his knock of 21 supporting Jewell in a 56-run opening stand.
Jewell, who pulled the ball with venom in an innings that included 11 boundaries, found another ally in Tim Ward, who finished the day unbeaten on 53.
It was Jewell's first Shield century of the summer and came at just the right time with regular opening partner Weatherald on Test duty.
NSW had earlier resumed on 2-214 after a rain-interrupted opening day.
Left-hander Kurtis Patterson added just one to his overnight tally before being run out for 80.
From there the visitors were able to keep chipping away to take wickets at regular intervals but Lachlan Shaw (68) and Josh Philippe (52) ensured NSW reached a solid total before their declaration.
Tasmania quick Riley Meredith finished with 3-77 to take his season tally to 15 wickets in just five innings.
The consistency of the 29-year-old paceman has been a highlight this season where he has captured three wickets in an innings on five occasions.
Meredith, who took a career-high 23 wickets in just six matches in the Shield last season, is returning to the form that led to him representing Australia in both ODI and T20 internationals.
