Australia were 463-6, heading New Zealand by 280 on the first innings at stumps on the second day.
Khawaja was out for a classic 140 and Voges, given a life on seven, was unbeaten on 176.
The 36-year-old Voges, in his 19th Test innings, saw his Test average rise to more than 100, bettering Don Bradman's 99.94 from an 80-innings career.
Voges has scored centuries in his last three innings, posting 269 runs not out and an unbeaten 106 against the West Indies in December.
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For his part, since his recall to the Australian side last year Khawaja has averaged 128.80 from six innings which include four centuries.
The single highlight of the day was a stunning caught and bowled by Trent Boult to dismiss Mitchell Marsh, but that occupied a split second on a day where the bat otherwise dominated.
Voges and Khawaja's firm grip on the game in a 168-run stand for the fourth wicket left New Zealand with few moments to relish on a day of toil under the baking sun.
BJ Watling missed a stumping opportunity when Khawaja was on 34 and Mark Craig was confident with an lbw appeal that was turned down when Khawaja was on 104.
A review showed the ball would have grazed the outside of leg stump and the umpire's original not out decision remained.
Voges had his moment of luck in the last over on day one when he was bowled by Doug Bracewell, only for umpire Richard Illingworth to wrongly call the delivery a no ball.
Boult hinted a fightback for New Zealand was possible
But the euphoria in the New Zealand camp quickly disappeared as they laboured through another 27 overs and 96 runs before Peter Nevill was the next wicket to fall.
Boult outsmarted Khawaja by bowling wide of the crease and as the left-handed batsman shaped to turn the ball to the on-side it straightened and slammed into the back pad.
Marsh was out to a spectacular catch off the second ball he faced when he drove hard at a Boult delivery, and the left-arm paceman flung himself high to his right to snare the ball in his right hand.
Australia had resumed the day on 147-3 and added 91, 92 and 133 in each of the three sessions on a flattening pitch.