Labuschagne posted an unbeaten 67 and shared partnerships of 100 with Pucovski and 60 with Smith (31 not out) after going to the crease in the fourth over.
With the series tied 1-1 at the halfway point, Australia won the toss and elected to bat Thursday at the Sydney Cricket Ground.
It gave Pucovski an immediate taste of Test cricket as the 22-year-old opener started the innings with veteran David Warner, who has been sidelined for more than a month with a groin strain.
Warner lasted only eight balls and scored five runs, and appeared slightly tentative taking a quick run, before he chased a full and wide ball from Mohammed Siraj and was caught at first slip with the total at 6.
Australia hasn’t posted a total above 200 so far in the series and Warner’s early dismissal could have spelled more trouble, but 22-year-old Pucovski appeared assured and his innings should set a platform for a decent first-innings total.
Also read: Stakes high, tension builds for Australia vs India 3rd Test
He had withdrawn from Test selection calculations in the previous two seasons because of personal issues and also struggled with concussion, but he put that behind him to anchor a 100-run second-wicket stand with Labuschagne — Australia’s biggest partnership so far in the series.
He was on 14 when play was suspended after 7.1 overs because of rain, beginning a lengthy delay that resulted in 35 overs being lost across the day.
The Australians resumed at 21-1 after the break and continued playing their shots, and at times Pucovski was lucky to still be at the crease.
He had three reprieves on his way to 50, a milestone he passed in the over before tea with consecutive boundaries against Navdeep Saini — the first two balls in Test cricket for the Indian fast bowler.
Also read: India on cusp of winning 2nd Test against Australia at MCG
He survived a pair of dropped catches from wicketkeeper Rishabh Pant on 26 and 32 and a missed chance for a run out on 39 before running out of luck when he was trapped lbw by Saini for 62 in the 35th over, giving the Indian paceman his first Test wicket.
Smith had a high score of 8 and a total of 10 runs in the first two Tests but a change in his grip and more attacking attitude, particularly against the spin of Ravichandran Ashwin, saw him returning to form.
“I was positive. I wanted to put him under a little bit of pressure, which I probably haven’t done so far in this series,” Smith said. “Nice to get one away and sort of free things up a little bit.
Also read: India could make up to 5 changes for 2nd test vs Australia
“It was a good day for Australia. I thought (Pucovski) played exceptionally well early. Marnus played well. Hopefully we can build on that tomorrow.”
Ashwin went wicketless — although he had Pucovski dropped off his bowling — and returned 0-56 from 17 overs. Saini had 1-32 from seven overs. Siraj also had a chance put down by Pant and returned 1-46, while Jasprit Bumrah returned 0-30 from 14 overs.
The Border-Gavaskar trophy is still up for grabs, with holder India hoping to secure it with a victory in Sydney and Australia needing to win the series to reclaim it.
Also read: Australia plans no changes for 2nd cricket test vs India
Australia won the opening day-night match in Adelaide by eight wickets and India responded with an eight-wicket win in Melbourne last week.