Head, who has resumed on his overnight score of 25, added 68 for the fifth wicket with Steve Smith (85), before sharing a vital 147-run partnership with skipper Tim Paine for the sixth wicket despite a barrage of bouncers from the Kiwi quicks.
Stylish left-hander Head has hit nine boundaries off 216 deliveries. The 25-year-old is just two runs short of his second century in his 16-test career, in an innings which has likely put to rest recent speculation over his place in the side.
Paine, who has captained Australia in 18 of his 30 tests, has crunched nine fours in his 77 not out and is edging towards his maiden test century.
Earlier, fiery New Zealand pace bowler Neil Wagner (2-68) bounced out Smith to deny the star batsman a fifth consecutive test century at the Melbourne Cricket Ground as Australia battled its way to 336-5 at lunch.
World No.2-ranked batsman Smith fended a bouncer from Wagner to gully where he was caught for 85, having taken more than an hour on Friday to add only eight runs to his overnight score.
Smith's patient, 242-ball innings included eight fours and one six. The right-hander had scored a century in the Melbourne test in 2014, 2015, 2016 and 2017, before missing the 2018 match because of suspension.
Head was joined by Paine who showed a willingness to attack against the short ball. The pair feasted after lunch on the bowling of spinner Mitch Santner (0-79) as Australia marched towards an imposing first-innings total.
Australia had resumed on Friday's second day of play on 257-4. New Zealand captain Kane Williamson had won the toss on Thursday and elected to bowl first in a bid to take advantage of the green-topped pitch and overcast conditions.
However, after the loss of Joe Burns (0) who was bowled by Trent Boult in the opening over, Australia consolidated as David Warner (41), Marnus Labuschagne (63) and Matthew Wade (38) battled hard on what Smith labelled a "difficult wicket".
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.