Before a huge Boxing Day crowd of almost 70,000, Smith joined teammate David Warner in reaching 1,000 Test runs for the calendar year with his unbeaten 72.
At the close, Australia were 259 for five after winning the toss with Brad Haddin seeking a confidence-boosting innings as the other not out batsman on 23.
Smith passed 50 for the fourth time in five innings in this series among them an unconquered 162 in Adelaide and 133 in Brisbane. So far he has amassed 447 runs at 223.5 for the series.
Smith, who won his first Test as skipper in four days in Brisbane last weekend, was well positioned for his third ton of the series after Rogers and Watson missed out on cashing in on solid starts.
Rogers hit his third straight half-century of the series and Watson made 52 in a 115-run stand before they were dismissed five minutes apart in the hour after lunch.
The pair had put on 59 runs off 131 balls for the fourth wicket.
Rogers, who scored 116 in last season’s corresponding Boxing Day Test against England, pushed at paceman Mohammed Shami and was snapped up behind by M.S. Dhoni for 57.
Watson followed six balls later in off-spinner Ravichandran Ashwin’s seventh over with an ill-judged sweep shot and was out leg before wicket for 52 in 89 balls.
Watson had a let off on 37 nearing lunch when Shikhar Dhawan fumbled him at second slip at the third attempt off Shami.
It was Watson’s 23rd half-century in Tests with just a below-par conversion rate of four centuries in his 55th Test for the senior top order batsman.
It was the 27th time in 102 Test innings Watson had been dismissed leg before wicket.
Shaun Marsh again failed to go on after a solid start and was caught behind by Dhoni off Shami with no addition to his tea score of 32 off 83 balls.
Debutant Joe Burns was given a rousing welcome as he came out to bat at four wickets down and got a roar with his first scoring shot off Shami for three.
Burns hoisted Ashwin over mid-wicket for four in a positive show of confidence at Test level.
But he lasted 27 balls before he attempted a pull shot on 13 and bottom-edged through to Dhoni off Yadav.
Warner, who scored twin tons in the opening Adelaide Test, was out in the second over of the innings.
He only lasted six balls before he played across Umesh Yadav and edged to Dhawan at third slip for a duck.
Shami and Yadav finished with two wickets each.
India made two changes from the team that lost the second Brisbane Test, with debutant Lokesh Rahul and Mohammed Shami coming into the side.
Rahul, who replaced Rohit Sharma, was selected to bat at number six, while speedster Varun Aaron made way for Shami, who was off the field for injury treatment late in the day.
Dhoni’s tourists trail 2-0 in the four-match series after defeats in Adelaide and Brisbane, and have not won at the MCG for 33 years. (AFP)