The 33-year-old twice trailed Huesler by a set but fought back before kicking away for a 6-7 (8-10) 7-5 6-7 (2-7) 6-2 6-3 win, prevailing in four hours and six minutes.
It sets up a likely second-second round show-stopper against two-time Australian Open finalist Daniil Medvedev on Wednesday, with the star Russian taking on American Marcus Giron on Monday night.
Millman, who required a wildcard after falling to No.140 in the rankings, joins fellow Australian Jason Kubler in reaching the second round of the men's draw on the opening day.
It is the sixth time Millman has reached the second round at his home major, in his ninth Melbourne Park campaign and 30th grand slam.
The first three sets lasted an hour, 47 minutes and 59 minutes respectively.
Millman led 5-0 in the opening set tiebreak but lost it 10-8, then had to do things the hard way from there.
He only needed another 80 minutes to wrap up the final two sets in front of a raucous crowd on Court 3.
Millman had three match points and spurned two attempted smashes on the first, hit his second into the net, before sealing victory with a punishing forehand.
