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Victoria 1 for 124 (Harris 67*) trail Western Australia 466 (Bancroft 100, Short 87, Whiteman 82, Cartwright 70) by 342 runs
The pair put on 104 for the first wicket before Pucovski, who struck four boundaries and a six from 117 balls, was caught behind when fending a short leg-side ball just before stumps. He had earlier looked to be trapped in front during Jhye Richardson's second over but the umpire's finger stayed down.
Harris' mini-milestone continues his solid early Shield form - he scored 85 and 42 in a draw against South Australia last week.
The left-hander hit 11 fours and dominated his union with Pucovski, who was continuing his first-class comeback after ongoing concussion issues.
Earlier, Western Australia's batting tail wagged as Short whacked a career-best 87 and Hilton Cartwright made 70.
WA resumed on Tuesday at 5 for 290 and Cartwright soon posted his 19th first-class half-century. He found support from Corey Rocchiccioli, who struck three fours and a six in his 27, and the pair put on a handy 56-run stand for the sixth wicket.
Short, batting at No. 8, cashed in with a late flurry - his career-high knock included seven fours and three sixes as WA set an imposing total.
Spinner Todd Murphy (3-104) led the wicket-takers for Victoria with Mitchell Perry taking 2 for 59 and legspinning debutant Ruwantha Kellapotha claiming 2 for 122.
Western Australia survive Murphy scare after Handscomb declines chance of 300
Handscomb declared with him unbeaten on 281 after a record stand of 338 alongside Sam Harper
Handscomb rides his luck to pile up big century as bat continues to dominate
Marcus Harris also made a century while WA lost an injured Joel Paris from their attack
Harris leads solid reply after Short takes Western Australia to big total
Victoria's openers added 104 on a surface that is proving tough work for bowlers