A resurgent Steve Smith smacked his 27th Test century before being the last man out as India snared eight wickets on Friday then safely negotiated a fiery spell before tea to trail Australia by 312 runs on day two of the third Test.

On an overcast morning at the Sydney Cricket Ground, the hosts resumed at 166 for two after losing 35 overs to showers on day one, when David Warner was dismissed for five and Will Pucovski 62.

Despite more rain delays, they were going well until Marnus Labuschagne was out for 91, sparking a collapse with only Mitchell Starc (24) showing defiance as Smith made 131.

They were eventually dismissed for 338, with spinner Ravindra Jadeja taking 4-62 and Jasprit Bumrah and Navdeep Saini grabbing two each to keep India in the hunt with the four-Test series finely poised at 1-1.

India negotiated a tricky nine overs before tea to be 26 without loss.

Rohit Sharma, back in the side after a long injury absence, was on 11 and Shubman Gill 14.

Smith, who averages over 61, failed to reach double figures in the first two Tests at Adelaide and Melbourne but roared back to life on his home ground, reaching his ton off 201 balls before a late flurry as wickets tumbled around him.

He looked comfortable throughout, crunching a four off Bumrah on the first ball he faced from India's top bowler Friday to signal his intent.

He survived an ambitious lbw review on 41 before bringing up a patient century then letting rip, adding a quickfire 31 before being the last one to go, run out by Jadeja's fabulous direct hit.

Labuschagne resumed the day on 67 and Smith 31, with both men making the most of a relatively flat pitch to bring up a 100-partnership.

It was a typically gritty innings from Labuschagne on a ground where he scored 215 this time last year against New Zealand.

But as he closed in on a fifth Test century, he was bamboozled by Jadeja.

Facing a ball that took extra bounce, he thick-edged it to Ajinkya Rahane at slip, with the Indian skipper taking a sharp catch.

At the other end, Smith looked ominous and brought up a 30th Test half-century, drilling Ravi Ashwin down the ground before light rain set in.

On their return from 24 minutes off the field, following an earlier eight-minute break, Matthew Wade was undone by his natural aggression, recklessly skying a Jadeja ball to Bumrah.

Cameron Green went without scoring, trapped plumb lbw by Bumrah who then clattered the stumps of Tim Paine (1) with a beautiful delivery that nipped back.

Pat Cummins was bowled by Jadeja for nought as Smith began running out of partners. He found an ally briefly in Starc to ensure he made his century, before the tail enders were mopped up.