After amassing 481 in response to Victoria's first innings 256, WA began day four needing seven wickets to wrap up victory.
They reached their goal early in the third session on Saturday when the visitors were knocked over for 172.
Spinner Corey Rocchiccioli followed his first-innings 3-39 with a mesmerising 3-14 off 26.2 overs, which included 20 maidens, while seamers Cameron Gannon (3-54) and Aaron Hardie (2-40) also impressed.
Nightwatchman Mitchell Perry (43) valiantly dropped anchor for 57 overs to top score for Victoria.
Peter Handscomb (two) and Jonathan Merlo (two) both fell before lunch as Victoria crawled to 2-37 in the opening session.
A draw looked a possibility when captain Will Sutherland joined Perry and dug in for six off 75 balls before his vigil ended thanks to a moment of genius from Cameron Bancroft under the lid.
Test hopeful Bancroft, WA's top scorer with 122, was described by Australia legend Steve Waugh in 2019 as "the best short leg (fielder) I've ever seen" and he lived up to that billing when he plucked a stunning right-handed catch to intercept Sutherland's pull off a Liam Haskett bouncer.
Cameron Bancroft 😲— cricket.com.au (@cricketcomau) That is a something special under the lid at short leg #SheffieldShield pic.twitter.com/2kHChKKrtbOctober 7, 2023
Todd Murphy was run out from Teague Wyllie's direct hit straight after tea before Rocchiccioli fittingly ended the match when he returned to the attack and dismissed Victoria's No.11 Scott Boland for two.
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