They are the first defendants to go on trial since seven soccer officials were arrested at Baur au Lac hotel in Zurich in May 2015, exposing what investigators say was a quarter of a century of corruption.
Napout's lawyers argue that the government was able to find no irregularities in his bank records, but prosecutors maintain he demanded to be paid in cash.
In his opening statement, Keith Edelman, US assistant attorney, said the case against the three defendants would focus on the way TV, sponsorship and marketing rights were sold for the two South American tournaments, the Copa America and the Copa Libertadores.
Prosecutors haven't disclosed the names of their cooperators because of attempts, they say, to intimidate witnesses.
The U.S says the three got bribes and kickbacks from sports-media and marketing firms tied to matches, including World Cup qualifying events, in at least five South American countries. "But lurking under the surface are lies, greed and corruption".
Edelman said the government's case includes "detailed ledgers, contracts, emails, hotel records and more", and that the jury will hear witness testimony from media executives and other former Federation Internationale de Football Association officials who have already pleaded guilty to the conspiracy.
In essence, he said, the defendants used shell companies, offshore accounts and bagmen to hide their dealings.
At another 2014 meeting involving Burzaco, the cooperating marketing executive, and other people where the bribery scheme was discussed, Burzaco made it clear he knew they were breaking the law and expressed his misgivings, the papers say of yet another recording.
The case is being heard amid the sort of security usually reserved for mafia cases. Recordings appear to corroborate prosecutors' case against him.
The case is the first to go to trial since the scandal emerged more than two years ago.
Marin, 85, is the most high-profile of the defendants.
Sepp Blatter, president for 17 years, and other officials were ousted as the full scale of the problem emerged.
US prosecutors say Brazilian businessman Jose Maria Marin was a soccer official on the take - and wasn't always discreet about it.
'Rather than fix the harm done to the sport and its institutions, however, these conspirators engaged in the same unlawful practices that had enriched their predecessors, ' says the indictment.
"It's about time to- to have it coming our way", he said.
Prosecutors Monday painted three former worldwide soccer bigwigs as rapacious predators who cared more about lining their own pockets with illegal bribes than promoting a sport they claimed to love. "Do not convict him because others have behaved wrongly".
Charles Tillman, defence counsel for Marin, said his client was only ever an interim president of the Brazilian national federation, selected because he was the oldest vice president when the incumbent stepped aside.
"That's it. That's right", Marin said.
"[Marin] was on the field but not playing the game", Stillman said. Napout, 59, presided over the Paraguayan federation and was FIFA's president of South America's governing body.
Burga's attorney Bruce Udolf accused the government of using "too broad a brush" and sweeping up "lower-level people like Manuel under this RICO umbrella".