The Spanish world number two, 20, playing a tour-level match against a player younger than himself for the first time in his career, was leading 6-1, 6-1, 1-0 when his 18-year-old opponent had to pull out.
Alcaraz, who missed last year's tournament at Melbourne Park with an injury, said it was "not the way anybody wants to move on" after the lopsided contest, which lasted just 66 minutes on Rod Laver Arena.
"I missed the tournament last year," he said. "I was watching the matches at home from the couch, wishing to play in the second week here.
"This is the first time I have moved to the second week in Australia. It feels special."
Shang held serve in his first game but Alcaraz won the next six games to take the set, not facing a single break point.
The second set was also one-way traffic, with the Chinese player unable to live with Alcaraz's power and range of shots.
Shang needed a medical timeout when 4-1 down in the second set, receiving treatment to his upper leg, but lost the next two games to give himself a mountain to climb.
Alcaraz broke for a sixth time in the match at the start of the third set and in the next game, Shang decided he could not continue.
The two-time Grand Slam champion next faces Serbia's Miomir Kecmanovic, who is ranked 60th in the world and beat 14th-seeded American Tommy Paul in five sets.
