Widely expected to be the worst pitch of the three produced in the series so far, Smith made it look remarkably flat but would have worried about running out of partners when the visitors slipped to 4-140.
Maxwell, playing the fourth test of his career and first since 2014, steadied with his longest ever international innings in any format.
The allrounder finished 82 not out after facing 147 deliveries. He waited some 56 balls before striking a boundary.
It was a different kind of potency to what Maxwell has demonstrated in ODI and Twenty20 cricket, but exactly what Australia needed. Maxwell's dig was notably the highest score by an Australian No.6 since Smith's century against South Africa in 2014.
Kohli left the field early in the second session, having injured himself diving to stop a boundary. Vice-captain Ajinkya Rahane failed to inspire teammates or come up with fields that made Smith or Maxwell sweat.
The body language of Rahane, who threw the ball to part-timer Murali Vijay late and would have dismissed Maxwell for 74 if he opted for a review, suggested he'd almost ran out of ideas to dismiss the two well-set batsmen.
