Western Australia 300 (Inglis 116) and 3 for 372 dec (Bancroft 176*) beat Tasmania 169 (Webster 52) and 120 (Kelly 4-41) by 383 runs
The Sheffield Shield holders cruised to a 383-run victory at Bellerive Oval, with the hosts dismissed for just 120 early on the final day.
With five wins from eight outings, the win leaves Western Australia closing in on hosting the season decider for the second year in a row.
Bancroft made batting look easy in the second innings scoring 176 not out - more than Tasmania's entire team managed in either innings.
Bancroft's fourth century of the summer took his tally well past Test squad member Peter Handscomb at the top of this season's Shield run-scorer list.
"Cameron Bancroft is having an amazing season, he is so confident and his game is in such a good place and I'm sure an Australian call-up wouldn't be far away," said Whiteman.
Western Australia suffered a first defeat of the season last week in Adelaide, but their quality was on display over three-and-a-bit days in Hobart.
After being sent in to bat, Western Australia overcame a challenging start to post 300 with wicketkeeper Josh Inglis scoring 116.
"It is really pleasing after a disappointing week in Adelaide last week to bounce back like this," Whiteman said.
"After losing the toss and being asked to bat, it was a huge effort on day one and the bowlers were outstanding to take 20 wickets."
The in-form WA line-up will be bolstered by the early return of spinner Ashton Agar from India for their remaining matches - both at home - against Tasmania and Victoria.
"The incentive is a home final and a big goal for us," said Whiteman, with WA already guaranteed to host the upcoming One-Day Cup final.
Tasmania lasted just 5.2 overs on day four with top-scorer Beau Webster (30) the last wicket to fall.
Despite two defeats in their past three outings, Tasmania remain just one win behind second-placed Victoria.