After visiting captain Jordan Silk won the toss and inserted WA, Meredith claimed a superb 4-11 from eight overs and Webster took 3-31 as WA were routed for 115 from 30.2 overs.
Only four batters reached double figures, and none made it to 20.
In reply, Tasmania wasted no time in blasting to 1-117 from just 16.2 overs.
Openers Mitchell Owen (43) and Caleb Jewell (41no) ensured there would be no nervous moments chasing the modest target in combining for an opening stand of 76 from 9.1 overs.
Webster then followed his strong work with the ball by contributing an unbeaten 26 off as many deliveries as Tasmania humbled the home team.
WA's openers had put on just seven runs in 2.3 over when Meredith had Sam Fanning (3) caught behind, feathering an edge outside off stump.
Bowling medium pace, Webster found an edge behind down the leg side to remove Joel Curtis (8) to make it 2-35, triggering a collapse of 4-37.
Cameron Bancroft grafted to 19 off 35 balls before he edged a catch to Webster at second slip off useful quick Will Prestwidge (2-19), who then had Will Malajczuk caught behind for a duck.
WA then lost their last five wickets for just 24 runs, leaving Tasmania's top order to make batting look simple compared to the home side's woeful innings.
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