The 26-year-old Burns had resumed after the break on 78 and brought up his century, his second against New Zealand, when he edged between slip and gully off Matt Henry to notch his 12th boundary.
Joe Burns scored his third test century, while captain Steve Smith hit his 14th as Australia moved into a dominating position in response to New Zealand's first innings total on the second day of the second test on Sunday.
Burns, who had been given out earlier only to have the decision overturned on review, was on 126 with Smith on 79 as the visitors went to the break on 241 for two, 129 runs behind New Zealand's first innings of 370. At the time of this report, Australia were 291/2, with Smith on 103 and Burns on 140.
New Zealand's only success on a Hagley Oval wicket offering no assistance to swing, seam or spin, was when Usman Khawaja was snapped up in the first hour of play for 24 off Trent Boult, the pick of the hosts' bowlers.
Burns and Smith then combined in an unbroken 224-run partnership as New Zealand's bowlers toiled under a cloudless Christchurch sky.
The 26-year-old Burns had resumed after the break on 78 and brought up his century, his second against New Zealand, when he edged between slip and gully off Matt Henry to notch his 12th boundary. Burns was earlier given out caught behind on 35 but immediately asked for a review and television replays showed the Matt Henry delivery had brushed his forearm and not his gloves.
Smith was struck in the back of the head by a short Neil Wagner delivery in the final over before tea but looked well set to push on to another century, though the second new ball is due three overs into the third session.
New Zealand's first innings was anchored by a superb counter-attack led by captain Brendon McCullum, who blasted the fastest Test century, from 54 balls, on Saturday. Playing his 101st and final test, McCullum scored 145 while Anderson (72) and BJ Watling (58) added half-centuries after the hosts were reduced to 32 for three within 20 overs.
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