Alcaraz comes good after shaky start to make Australian Open third round
The 22-year-old Spaniard came through the arm-wrestle 7-6 (7/4), 6-3, 6-2 on Rod Laver Arena to set up a clash with France's Corentin Moutet or American student Michael Zheng.
But it was a struggle early on against a player 12 years older who has never won a career title.
"I knew he was going to play great. I mean, I know his level, I played him a few times already," said the world number one, who is bidding to become the youngest man to complete a career Grand Slam of all four majors.
So far, the Melbourne Park hard courts have proved his nemesis, failing to go past the quarter-finals in his four trips to Australia.
He crashed at that stage last year to Novak Djokovic and Alexander Zverev the year before.
"To be honest, it was tougher than I thought at the beginning. I didn't feel the ball that good. You know, the ball was coming as a bomb, forehand and backhand," he added.
"Really, really happy that I got through a really difficult first set and then I started to feel a little bit better on the court."
Hanfmann had never gone past round two in 16 previous Grand Slam appearances, but he started well, working a break point on the Spaniard's opening serve.
It was saved, but against the odds he got the job done on Alcaraz's next service game courtesy of the top seed firing down a double fault.
Alcaraz quickly regrouped with a monster forehand to break back but there was nothing to split them as it headed to a tiebreak.
The turning point came when Hanfmann netted a forehand on serve to give Alcaraz a 5-4 advantage and the Spaniard served to seal a marathon set that spanned 78 minutes.
The reigning French Open and US Open champion reset and quickly took a grip on set two as he began to find his rhythm, rattling through it in just 43 minutes.
Hanfmann was spent and needed a medical timeout for work on his left shoulder at the break.
He gamely carried on but Alcaraz, who won a Tour-leading eight titles last season, scored a break to move 3-1 clear and made no mistakes as he sprinted to the finish line.