The World Cup co-hosts seized a 3-0 halftime lead in front of a heaving sold-out crowd of 70,492 in Los Angeles, where Tom Cruise, David Beckham, George Lucas and Bill Gates were among the spectators.
Folarin Balogun scored twice after an early own goal from Damian Bobadilla.
Paraguay pulled one back through Mauricio in the 73rd minute, but it failed to halt the party at SoFi Stadium and live sites dotted around the country.
Gio Reyna added a stunning fourth goal for the hosts deep into second-half injury time, delivering a fitting exclamation mark ahead of their clash with Australia on June 19 (June 20, AEST).
It was a symbolic tone-setter for the US, who started the tournament amid high expectations after the appointment of Argentine supercoach Mauricio Pochettino.
"The first 45 minutes were amazing, difficult to find a team to play like this. So happy and so proud," Pochettino said.
Balogun, who was born in the New York borough of Brooklyn to Nigerian parents, joined Arsenal's academy at age 8 and represented England at the youth level.
The striker, who opted to play for his nation of birth ahead of England or Nigeria, became the first US player to score multiple goals in a World Cup game since 1930.Â
It equalled the Americans' biggest ever win at a World Cup, while it was the first time they have scored four goals in a World Cup game.
The US only managed a combined three goals from four matches at the 2022 World Cup in Qatar.
Christian Pulisic had an assist in a stellar first-half play-making performance for the hosts, who enthralled fans with their creativity and aggression.
The performance will do little to quell American pundits' predictions of a lopsided clash between Australia and the US in Seattle.
Former US players Landon Donovan and Alexi Lalas have been among those to fire barbs at the Socceroos, with the former even describing Australia coach Tony Popovic as "smug".
"I've seen all the US stuff, and I'm just sick of it, to be honest," Socceroos midfielder Connor Metcalfe said last week.
"Like all this talk - it's just - let's just wait for the game, whatever happens, happens. It's just so much rubbish and I'm just sick of it.
"We'll just wait and we'll play - it'll be a good game.
"We had a friendly against them (last October). It was tense, it was feisty, and probably going to be the exact same."
Australia start their campaign on Sunday, facing Turkey in Vancouver.
With AP
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