After being routed for 183 on day one, the Tigers took six wickets on Saturday to bowl WA out for 271 and reached 2-174 in their second innings by stumps.
The outlook was not so good when opener Tim Ward was dismissed without scoring in the first over of Tasmania's second dig, edging Joel Paris (1-39) into the slips.
Ward's four-ball duck added to his personal woes after he was out on the first ball of the match in the Tigers' first innings.
Jewell (98 not out) was yet to score when he was dropped by Hilton Cartwright off Cameron Green's bowling and cashed in on the chance.
He has whacked 14 fours and a pair of sixes from 101 balls so far, putting him on the verge of a sixth first-class century and first of the season.
Caleb Jewell is two runs shy of his first ton of the Sheffield Shield season for Tasmania. (Darren England/AAP PHOTOS)
Jewell and Charlie Wakim (72) combined for a 170-run partnership for the second wicket to claim the honours for Tasmania on day two.
But Wakim was needlessly out a few minutes before stumps when he was caught off Charlie Stobo (1-27).
The Tigers added 150 runs in the final session and lead by 86 with eight wickets in hand heading into day three, with Jordan Silk (four not out) at the crease alongside Jewell.
Earlier on Saturday, Paris hit an unbeaten 40 as the WA tail wagged to give the visitors a first innings lead of 88.
Beau Webster (3-30) and Riley Meredith (3-59) did most of the damage with the ball for Tasmania.
WA's Jayden Goodwin fell short of a maiden first-class hundred when he was caught behind off Meredith for 85.
The hosts will resume their second innings on Sunday as they push to host the Shield final.
The Tigers sit top of the table with three games to be completed, while WA are third having had an inconsistent title defence so far.
