South Australia, set an unlikely victory target of 366 at more than four runs an over, were dismissed for 170 with the home side winning by 195 runs on Friday.
Wright was Tasmania's star finishing with a career-best six for 25 from 23 overs.
Michael Bevan, Tasmania's 34-year-old gun recruit from NSW, made the first ball of the day a memorable one, bringing up his third straight hundred at his new home ground.
He was out next ball, caught trying to hit speedster Shaun Tait over the midwicket fence.
Bevan was named man-of-the-match for his double effort of 106 and 100, following his 167 not out in a losing side against Victoria last week.
Captain Dan Marsh plundering an unbeaten 58 before he declared the innings to set up the run chase.
Mark Cosgrove topscored for South Australia with 58.
In Hobart (final day): Tasmania 375 (M. Bevan 106, M. DiVenuto 91, D. Dawson 73; S. Tait 4-111, P. Rofe 3-50) and 280 for 9 declared (M. Bevan 100, D. Marsh 58 not out; T. Kelly 3-59, S. Tait 3-72) beat South Australia 290 (G. Manou 97, D. Cullen 42; X. Doherty 5-66) and 170 (M. Cosgrove 58, J. Smith 47, D. Cullen 31 not out; D. Wright 6-25) by 195 runs.