Fury, wearing shorts with the American stars and stripes, entered the ring to James Brown's Living in America.
Fury, 30, backed Schwarz to the ropes in the second, driving a right hand home to drop the German to the floor.
"I got a big man out of there by switching it up. He caught me with a couple but you can't go swimming and not get wet," said Fury, who now has 28 wins and a draw on his record.
"I came here to have fun and enjoy myself. I don't take it too seriously. I thought I put on a good show and the fans got what they paid for."
This was Fury's first outing since his controversial draw with WBC heavyweight champion Deontay Wilder in Los Angeles in December.
There will be many who feel 25-year-old Schwarz was over-matched, with British heavyweight Dillian Whyte quick to label the German a "chump" and the fight "a joke".
But this was billed as a showcase bout for Fury in what was his first contest of a lucrative deal with ESPN. The marketing of the former world heavyweight champion was there for all to see as he took off a black robe during his MGM Grand ring walk to reveal the US stars and stripes on a second gown.
This was all about enhancing his profile to the American market and the five minutes and 54 seconds of boxing that followed did no harm to the undefeated Briton's future earning power or damage his hopes of a rematch with Wilder.
In round one he pinged a sharp jab through the underdog's defence and threw smart hooks around the guard, with Schwarz walking forward gamely but landing little against the evasive 6ft 9in Fury frame.
And in the second, Fury showed his abundant ring craft when he willingly retreated to a corner before landing a left hook while swivelling out of the tight space to open up an attack.
It was the beginning of the end as seconds later he thrust a right hand into Schwarz's face, forcing a knockdown which was quickly followed by the conclusion as Schwarz stood a static target with shots raining in on him.
Fury was handed the microphone and - just as he did after ripping the IBF, WBA and WBO world titles from Wladimir Klitschko in 2015 - opted to sing Aerosmith hit I Don't Want to Miss a Thing.
"Tonight was great, I will enjoy it," he added. "We will get deals done, get another fight in and then we fight Wilder next year."
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