Virat Kohli congratulated Ajinkya Rahane after the stand-in India skipper scored an unbeaten century on day two of the Boxing Day Test with Australia in Melbourne.

Rahane was afforded two lives en route to an unbeaten 104 for India, who reached 277-5 and a lead of 82 before stumps was called prematurely due to rain on Sunday.

It was Rahane's 12th Test ton and eighth away from home, his latest hundred coming from 195 balls as the tourists took control of the second Test.

The 32-year-old is also just the second Indian batsman to score a century on his first match as captain in Australia, joining Kohli in achieving the feat.

And Kohli, who has flown back home on paternity leave, took to social media to hail his team-mate's impressive display at the MCG.

"Another great day for us," he posted on Twitter. "Proper test cricket at its best. Absolutely top knock from Jinks @ajinkyarahane88."

Rahane and Ravindra Jadeja (40 not out) put on an unbeaten stand of 104 runs for the sixth wicket to frustrate Australia, who dropped four catches on the second day.

Indian opener Shubman Gill believes the patient batting of Rahane and Jadeja could prove decisive in the Test.

"I think it was a really valuable knock [from Jadeja]. He went into bat when we were 170-something for five," Gill told ANI. 

"It's very easy for us to loosen up and let opposition back in the game. So, the partnership between Ajinkya Rahane and Jadeja was really important for us.

"The way Rahane played was so patient. This knock was all about patience. 

"When you are playing such a high-quality bowling attack sometimes you go in that shell and you are not able to score runs. It was a magnificent knock to watch"