The 30-year-old's 6-82 complemented his three-for in the first dig at the WACA. The Gloucestershire-bound veteran took all five wickets to fall to bowlers on the final day of an absorbing contest.
It was fitting that his final match-winning wicket to dismiss Jhye Richardson (46) came via a catch to wicketkeeper Jake Doran, who took eight for the match.
Doran also batted brilliantly with the tail in scoring 33 and 74.
The win for Tasmania keeps them in touch with second-placed Queensland on the ladder, while Western Australia remain bottom.
The hosts began Sunday on 4-197, needing 148 runs for victory. They did a great job to get as close as they did before being bowled out for 322.
Bell started with the old ball and his tactics were spot on, as was his execution.
The plan to target the stumps reaped dividends when Teague Wyllie (21) pushed at one that came in without getting forward and was out lbw.
Bell came around the wicket to left-handed wicketkeeper Joel Curtis who played on.
Aaron Hardie (56) was holding the run chase together before Bell, this time with the new ball, snared him in the gully.
Fast bowler Richardson was dropped on one at slip by Tim Ward off Jackson Bird and rode his luck. He lost Corey Rocchiccioli (one) to a direct hit run out by Tasmania captain Jordan Silk. At that point the visitors were 8-258 and still requiring 87 to win.
Bell's fifth wicket to dismiss Cameron Gannon (23) came courtesy of a brilliant diving catch by Doran to his right to end a threatening 55-run stand with Richardson.
Bell's sixth and match-sealing wicket came courtesy of a feather off the gallant Richardson's bat.
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