Burns was not out 126 and Smith, who took a fearful knock to the head in the last over before tea, was on 79 at the end of the second session.
With a flat wicket working in their favour, the pair added 174 runs to have Australia 241 for 2 at tea in reply to New Zealand's first innings 370 at Hagley Oval in Christchurch.
Burns brought up his third century in his 10th Test, sending a good-length Matt Henry delivery between slip and gully to the boundary.
New Zealand quicks Trent Boult, Tim Southee and Matt Henry had the better of the exchanges at the start of the day.
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Boult put an added spring in the step of the New Zealanders with the valuable wicket of Usman Khawaja for 24 in the fourth over of the morning.
With Australia two down for 67, Burns and Smith took a cautious approach through the first hour of the day before upping the tempo as the life drained from the New Zealand attack and from the wicket.
Smith was subjected to a sustained barrage of bouncers from Neil Wagner and was felled in the last over before tea.
But after receiving treatment he recovered to take a single off the next delivery. It was his second blow to the body after being doubled up earlier when struck in the midriff by Boult.
In two sessions of cricket on the second day, Khawaja's early wicket has been New Zealand's only success after Australia resumed the day at 57 for 1.
Boult had removed David Warner, the only other Australian wicket to fall, with a similar delivery the previous evening.
Burns received a vital reprieve after he was given out, caught behind, for 35 only for the umpire's decision to be overturned when replays showed the ball had glanced off his forearm and not the glove.
For New Zealand, Boult has been the only successful wicket-taker with two for 47 off 17 overs.