The Gypsy King was punch-perfect in the MGM Grand in Las Vegas, displaying blurring speed and agility to dodge the ponderous German's shots.
Fury confirmed his big plans for the rest of the year, insisting there will be one more fight before the highly-anticipated rematch against the Bronze Bomber.
"I got a big man out of there with the left hook," Fury said after his emphatic victory. "He caught me with a couple of shots, so fair play to him.
"It was amazing, I hope America enjoyed it. I'm not one of those who take myself too seriously. September 21st or October 5th, I think in New York, then I'll hunt down Wilder.
Tyson Fury vs Tom Schwarz in pictures
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"I won't look past today, but Bob and Frank will get deals done, then we'll fight Wilder early next year.
"I already beat him once so I'll beat him again, and he's going to get a fully match-fit, sharp Tyson Fury.
"It's the biggest fight in world boxing, and the biggest we'll see for the next few years. It doesn't get any bigger.
"It'll be brilliant to fight in New York (before then). I wanted to show a few things to the American public, to introduce myself properly.
"I showed a little bit of speed, boxing skill, my ability to slip and slide out of the way of punches and my ability to finish, which is important.
"I'm more active than I've ever been in my career, apart from the first year. I've always wanted to stay active, and I'm finally getting the opportunity to.
"I feel better with more weight on me, I put on an extra 10 or 11lbs from my last fight and I felt bigger and stronger for it."
Fury celebrates his win (REUTERS)
Former world heavyweight champion David Haye, who was previously scheduled to face Fury before injuries derailed the fight, was impressed by Fury.
"We didn't want a 12-round snooze fest, we wanted Schwarz to come at Tyson, which he did," said Haye.
Fury lands on Schwarz (AP)
"His class showed. It was punch-perfect and a statement of intent.
"I didn't know he possessed that spite when he had his man hurt. It looked crisp, sharp and powerful, Schwarz's face was messed up.
"He dismantled him!"
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