After all but 13.2 overs of the first day were washed out on Saturday in Brisbane, Head and Smith batted through the middle session to put Australia firmly in charge with their unbeaten 159-run partnership.
Smith, after struggling for much of his innings, reached 65 for his first half-century since he made 91 not out against the West Indies in January, again at the Gabba.
Head was simply superb and took the attack right up to the Indians, who had troubled all the other Australian batsmen in the hot and humid conditions.
The Indian attack bowled a lot straighter to Head than they did in Adelaide -- where he hit a sparkling 140 in a big Australia win -- but he was watchful early and punished any loose deliveries.
As his scoring rate increased, the Indian bowlers began to flounder and Head took full advantage, smashing 13 fours and taking just 115 deliveries on his way to his ninth Test century.
He was particularly harsh on recalled spinner Ravindra Jadeja, who bowled nine fruitless overs for 35 runs.
Australia resumed the day at 28-0 and lost the wickets of Usman Khawaja, Nathan McSweeney and Marnus Labuschagne in the extended first session.
The Indian bowlers, who were wasteful in their brief outing on Saturday, were much tighter on Sunday.
Khawaja has been struggling for runs at the top of the order and he had a torrid time playing and missing at the dangerous Jasprit Bumrah.
He added just two to his overnight 19 before Bumrah finally drew the faintest of edges through to wicketkeeper Rishabh Pant to leave Australia 31-1.
Bumrah struck again in his next over when McSweeney (9) edged a simple catch to Virat Kohli at second slip.
Labuschagne and Smith set about settling the innings, but with both players well below their best heading into the Test, the scoring rate was slow against the disciplined Indian attack.
Labuschagne faced 55 balls on his way to making 12 when he uncharacteristically went for an expansive drive off Nitish Kumar Reddy, only to get a thick edge to Kohli, who took a sharp catch at second slip.
The five-match series is level at 1-1.
