Hazlewood’s anger and obscenities were picked up by the stumps microphone as he challenged the umpires after an appeal for the wicket of New Zealand’s Kane Williamson was turned down.
An Australian team spokesman confirmed that Hazlewood had pleaded guilty to an International Cricket Council charge of dissent. The fine will be determined later.
There was no action against Australia captain Steve Smith, whose voice was also heard in the confrontation.
Australia go into the final day at 70-1 needing a further 131 runs to win the second and final Test and take the series 2-0, and go top in the world rankings.
Joe Burns is on 27 with Usman Khawaja 19. David Warner was out for 22.
Jackson Bird, with his first five-wicket Test haul, and James Pattinson combined to end the New Zealand second innings at 335, giving Australia a 201-run target.
– Tempers flare –
But it was a frustating day in the field for Australia as Williamson and Corey Anderson batted through the morning session and the possibility of an unlikely draw started to appear.
Tempers flared after a Hazlewood lbw appeal for the wicket of Williamson was rejected, with the Australians converging on umpires Richard Kettleborough and Ranmore Martinesz.
Bird said the angry reaction was due to frustration at not being able to take a wicket in the morning session.
“We bowled pretty well in the first session and we probably thought it was out, but those 50-50 calls either go your way or they don’t,” he said.
“It was probably the frustration of the whole session. We’d bowled pretty well and hadn’t got a wicket and we’d been pretty close a couple of times.
“Test cricket is a hard game and sometimes tempers can boil over and people can get frustrated.”
Although Australia are in a commanding position, New Zealand all-rounder Anderson said his side lived in hope.
“Hopefully we can go ‘bang bang’ and then potentially run through them,” he said.
Burns offered chances but luck was on his side. On 19, he pulled Matt Henry through square leg where Neil Wagner was unable to hold a difficult chance. On 23, an inside edge off Henry sailed close to off stump.
“We managed to run through the tail pretty quickly in the first innings after they’d put on about 400 for the first six wickets,” Anderson said.
“If we can get in a similar situation then we’ve just got to back ourselves.”
– Bird strikes –
Although Australia have been dominant for much of the Test, New Zealand put up a valiant fight with two century partnerships as they battled to save the contest.
Williamson made 97 when adding 102 for the fifth wicket with Anderson.
The loss of Anderson for 40 was the start of a triple Bird strike that claimed three wickets in six balls.
Williamson and Tim Southee also fell before BJ Watling and Henry mounted rearguard resistance, adding 118 for the eighth wicket.
Anderson, having pocketed his usual attacking instincts, occupied the crease for three hours before shelving caution and driving at a wide delivery which he edged on to the stumps.
When Bird took the new ball in his next over he bagged the wicket Australia had fought for all morning, bowling Williamson three runs short of what would have been a 14th Test century, and two balls later he removed Southee for a duck.
Where Williamson and Anderson had been the epitome of caution, Watling and Henry took a more aggressive route to disrupt the line of the bowlers who were finding some reverse swing.
Henry, in his fourth Test, had 12 fours in his 66, easily surpassing his previous best of 27.
For Australia, Pattinson removed New Zealand’s top order in his four for 77 and Bird finished with five for 59.