Smith remained 72 not out at the close, backing up his scores of 162 and 52 in the first Test in Adelaide and 133 in the second Test in Brisbane, as Australia began their push for a 3-0 lead in the four-match series.
Chris Rogers (57) and Shane Watson (52) also notched half-centuries for their hosts, while Umesh Yadav??and the recalled Mohammed Shami snared two wickets apiece for the tourists at the MCG.
Smith, standing in as Australia skipper once again for the injured Michael Clarke, won the toss in Victoria and elected to bat, but saw David Warner (0) depart before a run was scored, with the opener clipping Yadav to Shikhar Dhawan at third slip.
Rogers and Watson, though, put on a century stand for the second wicket before both were dismissed with 115 on the board ??? Rogers edging Shami behind to wicketkeeper MS Dhoni and Watson, who had been dropped on 37 by Dhawan, trapped lbw trying to sweep Ravichandran Ashwin.
Shaun Marsh (32) put on 69 runs with Smith but exited the crease when he was pouched by Dhoni, while Test debutant Joe Burns (13) ??? batting at six in place of hamstring-injury victim Mitchell Marsh ??? cracked two fours before he was also caught by the India skipper behind the stumps after miscuing a pull stroke.
Australia were teetering on 216-5 at that stage but Smith and the evergreen Brad Haddin (23 not out) saw the Baggy Greens through to the close with an unbeaten partnership of 43.
Smith amassed four fours and a six as he moved to within 28 runs of a seventh Test century, while Haddin also smacked a maximum as he carded his highest score of the series following failures in Adelaide and Brisbane.
India, who dropped Varun Aaron and Rohit Sharma in Melbourne and replaced them with Shami and debutant Lokesh Rahul, bowled tightly as they attempted to bounce back from their defeats by 48 runs and four wickets respectively in the opening two Tests.
But the visitors did have to cope without Shami late in the day when the 24-year-old underwent injury treatment at a ground where India have not won for 33 years.