Prodigious opener Yashasvi Jaiswal has been dramatically run-out in a chaotic mix-up with Virat Kohli that has wildly swung momentum Australia's way in the Boxing Day Test.

Instead of batting through the final session of day two, Jaiswal (82) and Kohli (36) were both dismissed in an eventful 30 minutes before stumps.

Cruising at 2-153, India lost 3-7 as the tourists went to stumps at 5-164, still trailing Australia by 310.

The carnage started when Jaiswal attempted to run after hitting a shot to mid-on, but Kohli turned back around when the talented left-hander was already halfway down the pitch.

Australia captain Pat Cummins threw the ball back to the keeper for Alex Carey to make the easiest run-out.

Rattled by being involved in running out his talented teammate, Kohli fell to Victorian hero Scott Boland (2-24) seven balls later when he nicked to Carey.

Boland has a record of 3-27 against Kohli during five Test innings.

The 35-year-old struck again when he removed nightwatchman Akash Deep in the second-last over of the day.

After smashing a supreme 161 at Optus Stadium, Jaiswal managed a combined 32 runs across the next two Tests in Adelaide and Brisbane.

The 22-year-old was surely on his way to a fifth Test century before being hung out to dry by Kohli.

A crowd of 85,147 turned out on Friday, breaking the day two record for a Boxing Day Test.

Only the MCG Test against West Indies in February 1961 had a bigger day two crowd - 90,800.

Cummins bowled in-form India batter KL Rahul (24) with the final ball before tea as the tourists slumped to 2-51.

After opening together in the first three Tests, Rahul shifted to No.3 in Melbourne to accommodate captain Rohit Sharma at the top with Jaiswal.

But a move back to opener failed to help Rohit out of his form slump, casting further doubt on his Test future.

Jaiswal and Rahul are the only members of India's top-six to score more than 200 runs in this series.

The 37-year-old Sharma fell to rival captain Cummins after an ugly, mis-timed shot to the leg-side, prompting fierce criticism from former stars in the commentary boxes.

Earlier, Steve Smith's late-career revival continued with the star veteran posting his 34th Test century to power Australia to 474.

After starting day two at 6-311, Australia added another 4-163 on Friday before being bowled out just after lunch.

Smith brought up tons in back-to-back Tests when he drove Nitish Kumar Reddy for four midway through the first session.

His innings ended on 140 off the seventh ball of the second session when he played on to his stumps against Akash Deep.

India piled on 6-487 in the second innings of their huge win in Perth, but have only made one other score exceeding 200 in the series.

Cummins (49) also added valuable runs, sharing a 112-run seventh-wicket partnership with Smith.

The 35-year-old Smith arrived at the MCG after scoring his first Test century since June 2023 when he hit 101 in the rained-out match at the Gabba.

It was Smith's 11th Test ton against India, adding to his 12 made in Ashes battles.

Smith overtook England star Joe Root (10) for most Test centuries scored against India.

It was also Smith's fifth Test hundred at the MCG, a venue where he has 1209 runs at an average of more than 86.

The former Australia captain seemed to be facing his cricketing mortality after making a combined 19 runs in the first two Tests of the series, which extended his Test century drought to 18 months.

Continuing on from an unpredictable start to the Test, play was briefly interrupted on Friday morning when a pitch invader wearing an Indian shirt ran onto the field and touched Rohit and Kohli.

Security eventually got to the man, but not before Kohli was forced to awkwardly interact with him.

Day two came after teenager Sam Konstas smashed an unforgettable 60 to begin his international career on Thursday, bravely taking on India's strike weapon Jasprit Bumrah (4-99).

Bumrah's 99 runs, from 28.4 overs, is the most he's conceded in an innings during his glittering 44-Test career.

India retain the Border-Gavaskar trophy if they pull off a comeback victory in Melbourne.

Australia need to prevent India from winning one of the last two Tests in this series, while claiming at least one themselves, to regain the trophy for the first time since 2014-15.