A Damian Bobadilla own goal within seven minutes sent them on their way before Monaco striker Florian Balogun scored a sensational brace to put his team 3-0 up before half-time.
Giovanni Reyna then completed the thrashing with a strike deep into added time after Mauricio bagged a 73rd-minute consolation.
It was the first time in 96 years that the USA had won a World Cup game by a three-goal margin, doing so on two occasions at the inaugural tournament in 1930.
Mauricio Pochettino's men were electric in attack against a beleaguered Paraguay back line, and it wasn't the only positive he will have taken from the match.
The tournament co-hosts were marshalled exceptionally in defence by Crystal Palace star Chris Richards, who completed all 83 passes he attempted on the night.
According to Opta, it's the most passes completed with 100 per cent accuracy by any player in a World Cup match since 1966.
The 26-year-old complimented his calmness and quality in possession with incredible defensive actions, including three clearances, three recoveries, and six duels won.