Sinner, who knocked out Schwartzman's compatriot Francisco Cerundolo (24) earlier this week, was sharp from the outset as he fended off three break points and punished his opponent with vicious forehand winners before breaking late to capture the opening set.
Sinner cruised from there on, using both serve and forehand to devastating effect as he controlled rallies from the baseline and frustrated Schwartzman, winning five straight games as errors crept into the Argentine's game.
Not even a lengthy halt in play to close Court One's roof could impede the Italian's momentum, as he traded breaks early with Schwartzman in the third before seizing the advantage and wrapping up the contest with his 15th ace of the match.
"I felt like I was serving very well in the important moments," said Sinner, who is chasing his first Major title after reaching the quarter-finals of three of the four Grand Slams last year.
"I tried to return as many balls as I could and I tried to play my game. Moving him around is not easy because he is so fast, so I tried to overpower him a little bit.
"Hopefully I can play some good tennis here, play point-by-point and then we'll see where I can finish."
Sinner will next face either Australian Aleksandar Vukic (27) or Frenchman Quentin Halys (26), but he will have to wait until Thursday to learn the name of his third-round opponent after the pair's match was postponed due to rain.
