After resuming on day three at 3-46, NSW worked hard at Bellerive to take the game into the final day and make the home side bat again.
But spinner Jarrod Freeman made the key breakthrough late in the final session, trapping Ben Dwarshuis lbw for 21 and ending his 51-run stand for the eighth wicket with Chris Green.
Freeman also had Chris Tremain caught behind for a golden duck, ending the match, with NSW dismissed for 311.
The visitors could only manage 181 on day one and Tasmania took control with their first innings of 493.
Tasmania are the only unbeaten side after five rounds and this is their third win.
They are on 28.77 points, with second-placed Western Australia on 25.22.
Ryan Hackney (44) and Matthew Gilkes (56) put on 82 for the fourth wicket early on Monday, raising NSW hopes that they could take the game up to Tasmania.
Ollie Davies top-scored with 62 and Green had his highest Shield score, an unbeaten 61 that featured 159 balls and 10 fours, as he and Dwarshuis batted deep into the afternoon.
But NSW lost their last three wickets in four overs and are second-last on the ladder.
Tasmania's Bradley Hope was man of the match for his unbeaten century and two wickets.
Lawrence Neil-Smith took 3-57 in NSW's second innings, while Freeman and Hope claimed two wickets apiece.
NSW will host Tasmania from November 28 in their next Shield game.
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