The 30-year-old landed several shots to the nose of Schwarz to bloody him, then sent him to the ropes where the German finally went down to one knee.
Schwarz returned to his feet but was powerless to evade a flurry of punches and his corner threw in the towel at about the same time the referee stepped in to stop the fight.
"The key to tonight was to enjoy myself," said Fury, whose career record now reads 28-0-1.
"I used the jab, I was slipping and sliding with my hands down, switched to southpaw and caught him with a straight left. It was a good shot, it would have put anybody away."
It was a first career loss for Schwarz (24-1) and an impressive statement from Fury in his first bout since his controversial draw with Deontay Wilder in December.
Fury said he would fight again this year in late September or early October, before a rematch with Wilder in 2020.
First, though, the 6ft 9in (2.06m) fighter showed the MGM Grand Garden Arena crowd his ability to entertain in his first performance on the Vegas Strip.
Fury switched to a south paw stance in the second round, then appeared to taunt Schwarz as he put his back to the ropes and eluded several punches with his hands down at this sides.
Moments later, he landed the big punches that ended the fight.
The show, however, was not over yet.
Fury had entered the ring wearing robe, trunks and hat designed in the American flag while the James Brown standard "Living in America" played.
He concluded the evening by grabbing a microphone and singing a rendition of Aerosmith's "I Don’t Wanna Miss a Thing".
Fury, who said he gained 12 extra pounds for the fight, delivered a strong performance just weeks after the shock of heavyweight Anthony Joshua being beaten by Andy Ruiz Jr. in a title bout.
Wilder also recently took the spotlight in a vicious knockout of Dominic Breazeale in May.
While Ruiz and Wilder own the heavyweight belts, Fury proved he is still a major factor in the division.
Fury has continued to work his way back from a 31-month layoff where he battled mental illness and weight gain.
Schwarz, who was fighting for just the third time outside Germany, received a visit from Fury near his dressing room following the fight.
"You came to win and that stands for a lot," he said.
(Writing by Jahmal Corner in Los Angeles; editing by Sudipto Ganguly/Nick Mulvenney)
