Tasmania 4 for 115 (Copeland 4-27) trail New South Wales 9 for 442 dec by 327 runs
Rain meant only 4.3 overs were possible on the third day at the SCG to hamper New South Wales' hopes of pressing for victory against Tasmania.
Trent Copeland, who claimed three wickets the previous evening, struck with the first ball of the day when George Bailey was caught behind.
Jake Doran and Matthew Wade survived through to the stoppage against Copeland and Nathan Lyon.
There was hope of a resumption before the scheduled lunch break, but as forecast heavy rain moved across Sydney and further action always appeared unlikely well before the call-off.