Tasmania 169 and 8 for 101 (Kelly 4-41, Paris 3-34) need 403 more runs to beat Western Australia 300 and 3 for 372 dec (Bancroft 176*, Wyllie 8-Hardie 58*)
Former Test opener Cameron Bancroft continued to issue a compelling case to national selectors with a flawless century before Western Australia's quicks ripped through Tasmania late on day three to close in on a sizeable Sheffield Shield victory.
Bancroft's unbeaten 176 from 280 balls at Blundstone Arena dominated WA's second innings of 3 for 372 declared as he posted his fourth century of the Shield season. He is the competition's leading run scorer this season with 739 runs at 61.58.
Set 504 runs off 120 overs, Tasmania's batting order crumbled under sustained seam bowling from Joel Paris and Matthew Kelly to reach stumps at a forlorn 8 for 101.
With Tasmania seven wickets down, WA claimed the extra half hour in a bid to wrap up victory inside three days but made just one further inroad.
A WA victory, however, is essentially a foregone conclusion with warm and sunny conditions forecast on Friday.
The 30-year-old Bancroft powered them into a commanding position and continued his strong domestic season, which also included being a key cog in Perth Scorchers' BBL title campaign. He notched his 23rd first class century but ran out of time to reach his third double ton.
With wicketkeeper-batter Josh Inglis unwell, Bancroft took the gloves for most of Tasmania's second innings and took a catch to dismiss former Test captain Tim Paine.
Bancroft, who played the last of his 10 Tests during the 2019 Ashes series, has been bandied around as a potential replacement for injured opener David Warner with selectors pondering reinforcements after big losses in the opening two Tests against India.
He issued a timely reminder with a brilliant knock to flatten Tasmania's strong attack. With WA resuming at 1 for 92, Bancroft reached his century in the second session with his innings marked by superb cover drives and a watertight defence.
He combined in a second-wicket partnership of 147 with teenager Teague Wyllie, who fell short of his second first class century when he was caught behind on 80 off allrounder Beau Webster.
Bancroft, however, remained unperturbed as he reached his 150 with a boundary on the first ball after tea as WA set their sights on a lead of 500 runs.
Allrounder Aaron Hardie launched before the declaration with a couple of sixes to finish 58 not out from 64 balls.
Having been bowled out for 169 in their first innings, Tasmania's batting woes continued when left-handed opener Tim Ward edged to third slip from Kelly who bowled around the wicket.
Kelly and left-arm quick Paris, who plays for Hobart Hurricanes in the BBL, conjured menacing seam movement and were almost unplayable with seven wickets combined.
Paris claimed Jake Doran and Ben McDermott on consecutive deliveries as Tasmania appeared set to be embarrassingly bowled out in a session.
Webster, however, mustered late fight to drag the match into a final day.
