Rain and some stubborn Tasmanian batting have stymied NSW on day two as the Blues seek victory to guarantee a Sheffield Shield final berth.
Rain at Hobart's Bellerive Oval at either end of the day meant one-third of Thursday's scheduled overs were lost, with Tasmania sitting at 2-117 in response to NSW's 375.
The second-placed Blues need to win to avoid potentially being leapfrogged by third-placed Western Australia in the race to meet Victoria in next week's season decider.
Tasmania's leading run-getters Alex Doolan and Matthew Wade ended the day in confident fashion, having put on an unbeaten 50 for the third wicket.
The pair were rarely troubled with opener Doolan posting his sixth half-century to finish on 54 not out and the prolific Wade on 17 not out.
Trent Copeland (2-35) made a double breakthrough just before tea after Jordan Silk (25) had been part of a 53-run opening stand.
Tasmania scored at just 2.5 runs per over during their innings, while NSW - missing injured spinner Steve O'Keefe - struggled for penetration.
The Blues' tail-enders added invaluable runs earlier in the day as the visitors advanced from their overnight 7-311 to be dismissed eventually for 375.
Sean Abbott led the way with a lusty 47 not out, while debutant wicketkeeper Baxter Holt added 25.
Tasmania's Shield campaign effectively ended with last week's narrow defeat to Western Australia.