Stand-in skipper Ajinkya Rahane rode his luck to hit a gritty unbeaten century as India built an ominous 82-run lead over Australia on day two to take a stranglehold on the second Test in Melbourne on Sunday.

It was a determined and crucial knock against a world-class attack by the mild-mannered 32-year-old, who assumed the captaincy from Virat Kohli after he returned home for the birth of his first child.

Batting at four, he faced 200 balls for his 104 to steer India to 277 for five before rain ended play 15 minutes early. Ravindra Jadeja was not out 40.

The hosts took just four wickets during a frustrating day in the field as the match began to slip away with India zeroing in on levelling the series after losing the first Test by eight wickets in Adelaide.

Mitchell Starc and Pat Cummins both took two wickets.

While Rahane was the hero, it was a gutsy team performance, with three 50-plus wicket partnerships to help silence their critics after India were skittled for their all-time low of 36 last week.

On a steamy and overcast day at the Melbourne Cricket Ground, they resumed on 36 for one in reply to Australia's first innings 195, having weathered a torrid 11 overs Saturday when they lost Mayank Agarwal for a duck.

In an action-packed morning, the Australian attack consistently hit its line and length with Pat Cummins bagging impressive debutant Shubman Gill for 45 and then the experienced Cheteshwar Pujara for 17.

That brought Rahane to the crease and -- first with Hanuma Vihari, then Rishabh Pant and finally Jadeja -- he built half-century stands to put India in a strong position.

He brought up his 12th Test ton in his 67th game, and his second in Melbourne, with a four off Cummins, but he enjoyed some good fortune.

- Problems -
Australia removed first slip during Starc's first spell in the final session and lived to regret it with Rahane getting an edge on 57 that would almost certainly have been caught if the fielder was there.

He had a huge let-off on 73 when he was dropped at second slip by Steve Smith and again on 104 when the ball popped out of Travis Head's hands as he landed after taking the catch.

Jadeja, back in the team after missing the first Test injured, ably supported Rahane at the other end after Vihari fell for 21 attempting to sweep Nathan Lyon, with Smith taking the catch.

That brought the exuberant Pant to the crease. Preferred to Wriddhiman Saha as wicketkeeper, he scored a breezy 29 before becoming Starc's 250th Test wicket, caught by Tim Paine for his 150th dismissal.

India were reduced to 64 for three before lunch after Cummins caused all sorts of problems.

He signalled his intent with the first ball of the day, which zipped past Pujara's bat. Paine called for a review, believing it took a nick, but replays showed it was not out.

Gill also survived a scare in the first over he faced with Paine at fault, failing to hold a difficult catch off Josh Hazlewood.    

Cummins finally got the wicket he deserved when Gill, who added 17 to his overnight score after being preferred as opener to the axed Prithvi Shaw, got a nick and Paine took a simple catch.

He then removed Pujara, again enticing an edge with Paine holding a brilliant diving catch.

Scoreboard
Scoreboard at stumps on day two of the second Test between Australia and India at the Melbourne Cricket Ground on Sunday:

India first innings (overnight 36 for one)

M. Agarwal lbw Starc                     0

S. Gill c Paine b Cummins               45

C. Pujara c Paine c Cummins             17

A. Rahane not out                      104

H. Vihari c Smith b Lyon                21

R. Pant c Paine b Starc                 29

R. Jadeja not out                       40

Extras (b12, lb6, w1, nb2)              21

Total (five wickets, 91.3 overs)       277 

To bat: Ravi Ashwin, Umesh Yadav, Mohammad Siraj, Jasprit Bumrah

Fall of wickets: 0-1 (Agarwal), 2-61 (Gill), 3-64 (Pujara), 4-116 (Vihari), 5-173 (Pant) 

Bowling: Starc 18.3-3-61-2, Cummins 22-7-71-2, Hazlewood 21-6-44-0, Lyon 18-2-52-1, Green 12-1-31-0 

Australia first innings

J. Burns c Pant b Bumrah              0

M. Wade c Jadeja b Ashwin            30

M. Labuschagne c Gill b Siraj        48

S. Smith c Pujara b Ashwin            0

T. Head c Rahane b Bumrah            38

C. Green lbw b Siraj                 12

T. Paine c Vihari b Ashwin           13

M. Starc c Siraj b Bumrah             7

P. Cummins c Siraj b Jadeja           9 

N. Lyon lbw b Bumrah                 20

J. Hazlewood not out                  4    

Extras (b10, nb3, w1)                14

Total (10 wickets, 72.3 overs)      195

Fall of wickets: 1-10 (Burns), 2-35 (Wade), 3-38 (Smith), 4-124 (Head), 5-134 (Labuschagne), 6-155 (Green). 7-155 (Paine), 8-164 (Starc), 9-191 (Lyon), 10-195 (Cummins)     

Bowling: Bumrah 16-4-56-4, Yadav 12-2-39-0, Ashwin 24-7-35-3, Jadeja 5.3-1-15-1, Siraj 15-4-40-2

Toss: Australia

Umpires: Paul Reiffel (AUS), Bruce Oxenford (AUS

TV umpire: Paul Wilson (AUS)