Old warrior Karlovic, 39 next month, served down 53 aces as he came through 7-6(3) 6-7(3) 7-5 4-6 12-10 in four hours, 33 minutes -- the longest match in the tournament so far.
He will face Italian Andreas Seppi in round three when he will be the oldest player to contest that round since Ken Rosewall, aged 44, in 1978 when the draw was only 64.
It is the second year running the giant from Zagreb has been involved in marathon match here, having banged down a Melbourne record 75 aces last year on his way to a first-round win against Argentina's Horacio Zeballos, sneaking the fifth set 22-20.
"I'm happy but also very tired," the 2.11m Karlovic, who towered over Sugita, told reporters.
"I was already feeling it at the beginning of the third set but I just focused on my serve."
Karlovic faced four break points in the second game of the deciding set but saved all four, one with a second-serve ace. He then struck decisively in the 21st game of the set when he moved forward to force a forehand error from his opponent.
He completed victory a game later with a nerveless backhand volley and now sets his sights on another battle.
Karlovic, a gentle giant off the court, said he still loved the combat and would keep playing as long as his serve keeps firing him to victories like Wednesday's.
"I still like it, that's why I'm still here and doing it," he said. "We'll see how much longer I carry on."
Turning his thoughts to Seppi, he said he was prepared for another slog.
"It's going to be very tough because he returns unbelievably," he said. "I will try to play my game and we will see. It's going to be very hot and that will make my serve a little faster. But it will not be easy."
(Reporting by Martyn Herman; Editing by Amlan Chakraborty/Nick Mulvenney)
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