Head made 114 and shared a vital 150-run partnership with skipper Tim Paine to tilt the game firmly in Australia's favor and then its quick bowlers ousted opener Tom Blundell (15) and World No.3-ranked batsman Kane Williamson for nine to leave the tourists in a shaky position at 44-2 off 18 overs at stumps on Friday.
After scoring seven previous half-centuries, Head was able to shrug off the tag of being wasteful by converting a good start into a century, but not before Neil Wagner (4-83 off 38 overs) had again bounced out Steve Smith (85) before lunch and trapped Paine lbw for 79 just after tea. It was Paine's highest score in his 18 tests as captain.
Mitchell Starc fell for one in the following over, with a nervous Head on 99, still seeking the second test century of his 16-match career.
The stylish left-hander settled his nerves as he calmly reached the milestone two balls later with a boundary to backward point. Head took off his helmet and raised both arms in triumph to the large appreciative crowd, likely putting to an end any speculation over his place in the side.
Head, who had many uncomfortable moments against New Zealand's short-pitched bowling tactics, was caught soon after at cover off Wagner's bowling for 114 off 234 deliveries, including 12 boundaries, as Australia lost 5-33 chasing quick runs.
Australia had resumed Friday well-set at 257-4, but for the third consecutive innings this series, Smith couldn't manage a Wagner short ball and was out for 85, denying the star batsman the chance to become the first player to score a fifth consecutive test century at the Melbourne Cricket Ground.
As Wagner had done, Australia's quicks were also able to extract plenty of bounce from the MCG pitch and had Blundell caught behind before Williamson top-edged a pull shot off the bowling of James Pattinson and was caught by wicketkeeper Paine at backward square leg to reduce the visitors to 39-2.
Incoming batsman Ross Taylor was given out lbw to Pattinson for one, but the decision was overturned on a video review. Taylor (two) and opener Tom Latham (nine) will resume on Saturday.
Australia leads the three-match series one-nil after claiming a 296-run win over New Zealand in the first test in Perth. The final test will be played in Sydney starting on Jan. 3.