Head scored a blistering 152 and Smith a gritty 101 at the Gabba in Brisbane to put Australia in a strong position to go 2-1 up in the five-Test series.
With rain forecast over the next three days, India seem to have virtually no chance of winning the match and can only realistically hope for a draw.
After all but 13.2 overs of the first day were washed out on Saturday, India started strongly with three wickets in the first hour.
But Head and Smith batted India out of the game despite a superb spell from pace spearhead Jasprit Bumrah (5-72) after tea with the second new ball.
"The way he can put the bowlers under pressure from the outset is incredible," Smith said of Head, who smacked a sparkling 140 in a big Australia win in the second Test.
"It's nice to get into a partnership with him. The scoreboard moves so quickly."
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