Khawaja resumed at 102 on day two with the total at 389-2, and helped the Australians add 93 runs for the loss of one wicket — skipper Steve Smith for 48 — during an overcast morning session.
Smith added only seven to his overnight score before he was bowled by a swinging Trent Boult delivery with the total at 399 after a grinding start in conditions aiding bowlers.
Adam Voges replaced Smith and scored an unbeaten 50 from 81 balls before the break. Australia was 482-3.
Southee was into his second bowling spell when he left the field with an irritation of a disc in his spine, adding to the pressure on a struggling bowling attack.
The New Zealand team said scans on Southee's back overnight didn't reveal the cause of the problem but the pace spearhead was hampered during his opening four-over spell and was clearly in pain when he was helped off the field after the first drinks break. He was undergoing treatment and the Black Caps were hopeful he would return during the test. Southee had been the pick of the New Zealand bowlers, returning 1-70 from 24 overs. Boult took the key wicket of Smith, but his figures ballooned to 1-107 as Australia picked up the run-rate later in the session.
Momentum has been with Australia since Smith won the toss to start his first test series as captain, and his apparently vulnerable top order led the way.
Vice-captain David Warner scored 163 and shared partnerships of 161 with Joe Burns (71), who was elevated to open in his third test, and 150 with Khawaja on the opening day.
Khawaja was more cautious on Friday morning than he was in a flourishing first afternoon, when he plundered two sixes and 10 boundaries to reach his maiden test hundred from 123 balls.
He had one close call, before adding to his overnight score, when Boult hit him on the back pad in the second over. The New Zealanders called for a review of the not-out decision, but replays showed the ball pitched outside off stump and was missing the stumps.
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