Ajinkya Rahane celebrated a gritty hundred as India capitalised on Australia's poor fielding display to claim a first-innings lead on day two of the Boxing Day Test in Melbourne.

Stand-in captain 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.

Australia were woeful in the field, dropping four catches at the MCG, where Mitchell Starc (2-61) was left visibly frustrated after Travis Head spilled a catch to dismiss centurion Rahane with what proved to be the final ball of the day.

India resumed on 36-1 – in response to Australia's 195 in the second Test – after dominating the opening day in front of a capped Melbourne crowd and the tourists only lost four wickets to take control.

Shubman Gill (45) and Cheteshwar Pujara (17) did not last long as India fell to 64-3 following a masterful spell of bowling from star Australia paceman Pat Cummins (2-71), before the patient and anchoring Rahane got to work in the middle.

Tim Paine put down Gill in the second over of the day off the bowling of Josh Hazlewood (0-44), but the Australia captain made amends when he combined brilliantly with Cummins for two wickets.

Hanuma Vihari added 21 runs before he was sent packing by spinner Nathan Lyon (1-52) – bringing Rishabh Pant to the crease.

Explosive wicketkeeper Pant produced an entertaining 29-run cameo off 40 deliveries, but it came to an end when Starc broke through for his second wicket of the innings.

It brought up a milestone for Starc, who celebrated his 250th Test wicket, as Paine recorded his 150th dismissal.

Supported by Ravindra Jadeja (40 not out), Rahane posted his 12th Test ton and eighth away from home following the tea break – a boundary bringing up a memorable hundred from 195 balls.