Fury dropped the German to the floor after backing him into the ropes in the second round, before Schwarz's corner threw in the towel. "We will have another fight (on October 5), then we will fight Wilder".
"I came here to have fun and put on a show and I hope everybody enjoyed it as much as I did", Fury said.
Fury's British promoter Frank Warren was equally enthusiastic about the future for his fighter who is on the comeback trail after spiralling out of control following his 2015 win over Wladimir Klitschko, a result that ripped the heavyweight division open.
But Fury still intends to put on a show. "I put on an extra 12 pounds, and I could really feel (the power)".
Meanwhile Fury told BBC Radio 5 Live: "You're going to see more of Tyson Fury coming in".
Channeling his inner Apollo, Fury made his way to the ring dressed head to toe in stars and stripes, with a top hat to match, similar to what Carl Weathers' character wore in the Rocky films.
"I've come back from a dark place; this one's for you".
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Both are showing symptoms of the disease, from muscle pain and headache to vomiting blood, according to the ministry. Health teams in Uganda "are not panicking", Henry Mwebesa, the national director of health services, told the AP.
This was all about marketing Fury to an American audience - and the five minutes and 54 seconds of boxing nearly took a back seat.
Schwarz, who was fighting for just the third time outside Germany, received a visit from Fury near his dressing room following the fight.
It will be some occasion, certainly a more competitive one than this bout, which saw Fury extend his unbeaten record to 29 fights by dismissing the previously undefeated German challenger Schwarz and earn around £10 million in the process.
After the bout, the victor sang Aerosmith's "I Don't Want to Miss a Thing" for his wife and happy fans.
"There are two networks, and it's 50-50. He caught me with a couple but you can't go swimming and not get wet", said Fury after the fight. "Right here [in Las Vegas]".
"Now that he's in shape, he can knock out every heavyweight in the world".
Schwarz, who was fighting in the United States for the first time and facing a top opponent also for the first time, was a heavy underdog looking to pull an enormous upset that would have been even bigger than the one Andy Ruiz Jr. pulled on June 1 in NY when he scored four knockdowns and shockingly stopped Anthony Joshua in the seventh round to take his three heavyweight world title belts in a shocker.