After the home side scored at more than five an over and declared early on Saturday at 9-500, Tasmania scored at less than half that run rate in their second innings.
Tim Ward was on 49 from 169 deliveries and Teague Wyllie had made 33 off 80 balls in their 47-run partnership at Cricket Central. Tasmania need another 52 to make NSW bat again on the final day.
Bowling around the wicket, NSW quick Sean Abbott produced a pearl of a delivery to bowl opener Caleb Jewell for 88.
The breakthrough left Tasmania 2-156, before Ward and Wyllie steered them through to stumps.
After rain early in the day, the weather cleared and NSW resumed at 6-441.
Jack Edwards added another six runs before Marcus Bean had him caught by Jake Doran for 115 off 182 balls with 14 fours - his fourth Shield ton.
His departure gave Bean a five-wicket haul in his Shield debut and he finished with 5-111.
Ollie Davies top-scored on Friday with his rollicking 253.
Gabe Bell then picked up two wickets before NSW declared, giving them a first-innings lead of 255.
Tailender Reiley Mark hitting a quickfire 24 from 22 balls, with two fours and two sixes.
After going cheaply in the first innings, Tasmanian captain Jordan Silk chopped on and was bowled by Edwards for 16.
But the NSW attack was made to toil without reward in the hotter late-afternoon conditions.
If there is to be a result, it will come late on the final day unless NSW can somehow engineer a Tasmanian batting collapse.
20°C