Alcaraz destroys Gasquet to reach Australian Open second round
The second seed, gunning to unseat 10-time champion Novak Djokovic from the world number one spot, was tested in a tight first set but then moved through the gears.
Alcaraz said it was good to be back in Melbourne, where he has not been beyond the third round in his previous two visits.
"In the first set I struggled a little with his game," he said. "He was playing great but I played better and better and at the end I reached quite a good level."
The Spaniard admitted he sometimes tries to play "impossible shots", including volleys and drop shots, to please his fans.
Clad in a sleeveless yellow T-shirt, the two-time Grand Slam winner squandered nine break point opportunities in the first set but was rarely in trouble on his own serve.
The tie-break was a tight affair but Alcaraz, playing his first match of the season, capitalised on his first set point, hitting a forehand winner at the net.
The Wimbledon champion, who missed last year's Australian Open through injury, raced through the second set in 30 minutes, breaking Gasquet's serve twice and showing his full range of shot-making.
It was a similar story in the third set - 37-year-old Gasquet offered occasional glimpses of his rare talent but was given the run-around by a man 17 years his junior.
Alcaraz was briefly held up when serving the match but sealed victory with an ace before thanking the packed crowd at a rapt Rod Laver Arena.
He will next face Italy's Lorenzo Sonego.