Chris Tremain claimed a late wicket as Tasmania began their chase of 290
Tasmania 213 and 1 for 19 need 271 more runs to beat New South Wales 276 and 9 for 226 dec (J Sangha 75, Gilkes 64)
The home side declared late in the final session, leaving a target of 290 in 110 overs with the forecast not great on Monday, and claimed an early wicket when Chris Tremain continued his excellent match by trapping Caleb Jewell for a duck in the fourth over.
They had started the day with a lead of 71 but were set back early when Ryan Hackney got an inside edge and Kurtis Patterson nicked an excellent delivery from Sam Rainbird.
Gilkes, who was given three lives, and Sangha then added 70 for the third wicket to take New South Wales into calmer waters although Tasmania kept chipping away during the afternoon. Gilkes was bowled having a heave at left-arm spinner Tom Andrews who claimed his second when Jack Edwards chipped to cover.
A fifth-wicket stand of 51 between Sangha and Peter Nevill consolidated for New South Wales before Nevill edged a lifting delivery to slip shortly before tea in a sign batting could be tricky on the final day.
Sangha might have had visions of a late push towards a century but was given caught at short leg against Andrew from a delivery he clearly did not think he had hit.