The Spanish superstar won 6-3, 7-6(2), 6-2 on Rod Laver Arena, blasting eight aces and 38 winners to set up a second-round clash with Germany's Yannick Hanfmann.
But he also made 36 unforced errors, more than his 81st-ranked opponent.
"First of all, I'm just really, really happy to step on the court once again for the first time this season," he said, having only played a light-hearted exhibition against great rival Jannik Sinner in the lead-up.
"It couldn't be better to be on Rod Laver Arena.
"It was a good match," he added. "I think Adam pulled out some great shots, great level in the match, so I had to stay there too.
"Overall I'm just happy that I played as well as I played today. It felt like he was one step forward of me, he was always in a good position.
"He was solid from the baseline, his flat ball was really difficult for me. It was a really solid match."
Top seed Alcaraz already has six major titles aged just 22, but success on the Melbourne Park hard courts remains a glaring hole in his resume.
He has not made it past the quarter-finals in four trips to Australia, losing at that stage last year to Novak Djokovic and Alexander Zverev the year before.
Should he snap his Australia drought, Alcaraz would become the youngest man to bank a Career Grand Slam, surpassing retired compatriot Rafael Nadal, who secured all four majors by the age of 24.
He would also be the youngest man in the Open era to win seven Grand Slams since Bjorn Borg, aged 23.
The writing was on the wall for Walton, with Alcaraz never losing in the first round of a Slam, but the 26-year-old gave him a thorough examination.
The reigning French Open and US Open champion started steadily, probing for openings.
He worked four break points and finally converted on the fifth in game eight with a sizzling forehand winner before serving out for the set, showing unmatched speed and court coverage.
But against the odds, Alcaraz slumped 3-1 down in the second set as Walton held his own.
Alcaraz, who won a Tour-leading eight titles last season, fought back, but the Australian took his highly fancied opponent all the way to a tiebreak, where the Spaniard clicked into another gear.
He carried the form into the third set, where he broke to love for a 4-2 lead and coasted home.
