After being skittled for 167, WA appeared to be containing Victoria at the Junction Oval when the hosts were 6-207 on Saturday.
But No.9 Xavier Crone hit an unbeaten 62 from 65 balls, smashing three sixes to help Victoria reach 373.
Fellow bowlers Fergus O'Neill (44) and Sam Elliott (26) also chipped in to make WA's bowlers toil in hot conditions for most of the day.
Opening bowlers Joel Paris (3-44) and Cameron Gannon (3-59), as well as spinner Corey Rocchiccioli (3-115) took all but one of WA's wickets.
WA had to bat for the last hour before stumps on Saturday, reaching 1-33 with Sam Fanning and Jayden Goodwin at the crease.
Opener Cameron Bancroft, who has endured an unfortunate form slump after dominating the Shield for the past two seasons, struggled again.
After recently being overlooked for a call-up to the Test team for the first time since the 2019 Ashes, Bancroft fell to O'Neill for 11.
In the first innings on Friday, Bancroft could only manage 12, also losing his wicket to O'Neill.
Victoria have set themselves up nicely to become the first team to beat WA in the Shield this season.
WA are aiming to claim a fourth straight title, and were undefeated after three matches before they headed to Melbourne.
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