Smith elected not to enforce the follow-on after Darren Bravo and Carlos Brathwaite fired a spirited West Indies first innings that ended on 271, having been 91-6 overnight.
Australia, which scored 551-3 in its first innings, went to stumps at 179-3 in its second and likely to declare early Tuesday. Smith will resume day four on 70 not out with Mitchell Marsh on 18.
An Australian win still appears the most likely outcome, but the West Indies did well merely to force the game to a day 4, having been in a dire predicament going into Monday's play.
Bravo made a patient 81 and was the last man out at tea, and Carlos Brathwaite rode his luck to make 59 in his test debut as the pair shared a 90-run seventh-inning stand.
After Brathwaite was caught and bowled by off-spinner Nathan Lyon (4-66) with the last ball before lunch, Bravo stubbornly anchored his team's tail to restore some badly needed respectability.
James Pattinson (4-72), who appeared to dismiss Brathwaite twice in the morning session — one clean bowled and the other caught at long leg — only to have both deliveries called for no balls, broke through with the new ball after lunch by trapping Kemar Roach lbw for 22 with full-pitched delivery.
Jerome Taylor made an aggressive 15 before being caught behind off Lyon, and the innings ended when Bravo sliced a Pattinson ball to Steven Smith at gully.
Bravo's dogged knock held the innings together, facing 204 balls over almost a day's play and driving eight boundaries.
The West Indies bowlers continued the momentum in the final session, showing significant improvement on their poor efforts in the first innings and in the series opener in Hobart.
First-innings centurion Joe Burns lasted just two shaky overs before nicking a Jason Holder out-swinger to Kraigg Braithwaite at second slip for 4.
Fellow-opener David Warner made another early exit, scoring just 17 before becoming Carl Brathwaite's first test wicket when he was caught by Holder at gully.
Khawaja shared a quick-fire 77-run stand with Steven Smith before offering a top-edge to wicketkeeper Denesh Ramdin off Holder for 56.
Brief Scores (for full scorecard click here)
Australia: 551 for 3 declared (Usman Khuwaja 144, Steven Smith 134 not out, Joe Burns 128, Adam Voges 106 not out; Jerome Taylor 2/97).
West Indies 1st innings: 271 (Darren Bravo 81, Carlos Brathwaite 59; Nathan Lyon 4/66, James Pattinson 4/72, Peter Siddle 2/40).
Australia 2nd innings: 179 for 3 (Steven Smith 70 not out, Usman Khuwaja 56; Jason Holder 2/49).