Victoria started the day at 1-70 with a 160-run lead and are within touching distance of a big win after having WA 8-161, with the extra half-hour called before stumps on Day 3.
Despite some wobbles in the first session with Marcus Stoinis and Ashton Agar bowling well for the Alcohol.Think Again Western Warriors, Finch put the Bushrangers on course to victory.
He smashed 151 in 122 balls to remain unbeaten when declaring at tea with Victoria 8-378, setting WA 469 to win.
Victoria looked likely to wrap it up in the last session when WA was 8-99, but Josh Inglis (54) and Matt Kelly (24) survived to stumps with the Warriors 8-161 - still 307 runs behind.
After falling to 5-153 in the morning session, Finch and Cameron White (41) guided Victoria to lunch and, from there, Finch took off.
He brought up his century in 95 balls and then needed just 26 more to reach 150. It was his first century since November 2016 and first ever at the WACA Ground and included 16 boundaries and seven sixes.
Stoinis (4-82) and Agar (2-115) toiled hard for WA. But having Matt Kelly hampered by a back complaint and Simon Mackin uncharacteristically didn't help.
Victoria's pace attack was too good on a wicket offering plenty of assistance and with some cracks providing unplayable deliveries.
Tremain has backed up 7-82 in the first innings taking 3-61 while Scott Boland claimed 3-44 and Peter Siddle 2-39.
Stoinis did well with the ball for the match but knows some loose shots with the bat and not keeping the pressure up long enough with the ball has been costly.
"Obviously it's disappointing," Stoinis said.
"There's a bit in the wicket and we didn't bowl as well as we should have, and haven't batted as well as we should have. You can't let a good side like Victoria off the hook and that's what we've done."