Daniel Hughes (61), Jack Edwards (44) and Sean Abbott (47 not out) all made valuable contributions with the bat as the Blues posted a first innings total of 375 in the must-win clash.
In response, the Tigers were bowled out for 255, with Edwards (1/17) and Moises Henriques (1/27) both picking up wickets.
Henriques backed up his performance with the ball, with a vital innings with the bat. His 49 off 69 balls put NSW in a position to declare before the start of play on Day 4, holding a 269-run lead.
Abbott was outstanding with the ball, making light work of the Tasmanian batting line-up as he picked up incredible figures of 7/45, securing a 149-run win for the Blues.
NSW will take on Victoria in the final at the CitiPower Centre in Melbourne on Thursday.