MEXICO CITY — The chants of “Brady! Brady!” started as soon as the New England Patriots got their first third-down stop, and the fevered fans at Azteca Stadium awaited Tom Brady’s first appearance in Mexico.

The chants kept up for most of the day as Brady felt right at home in the new environment.

Brady threw for 339 yards and three touchdowns to the delight of an adoring crowd, and the Patriots beat the Oakland Raiders 33-8 on Sunday.

“That was very much a surprise, especially seeing some of last year’s game they were very pro-Raider,” Brady said. “Seemed like there were a lot of Patriots fans here, so that was good to see.”

Brady completed his first 12 passes and picked apart Oakland’s suspect defense. The large contingent of Patriots fans in the well-divided crowd for a Raiders “home” game had plenty to cheer about as New England (8-2) dominated from start to finish.

After winning their debut trip to Mexico City last year against Houston, the Raiders (4-6) were completely overmatched in their return. The offense failed to score until Derek Carr threw a TD pass to Amari Cooper in the fourth quarter with Oakland trailing by 30 points.

“They don’t do anything special, they just do everything right,” Carr said. “You sit there and in the first half they don’t have any turnovers, I don’t think they had a penalty, and they do the little things right.”

Oakland’s defense was victimized by short passes by Brady and then beaten on a 64-yard TD to Brandin Cooks on the third play of the second half that gave New England a 24-0 lead.

“It was just a fiesta all over the field,” Patriots tight end Rob Gronkowski said.

There was a festive environment at the famed stadium, with loud cheers for both teams from the crowd of 77,357 fans and a notable buzz throughout the early portions. Much was made heading to the game about the differing approaches to playing in an elevation of 7,200 feet above sea level. The Patriots spent the week at the Air Force Academy practicing at an elevation of 6,621 feet, while the Raiders stayed home and opted to limit their time at high altitude.

In a game this lopsided, it probably didn’t play much of a factor, although the thin air might have helped Stephen Gostkowski set a New England record with a 62-yard field goal at the end of the first half that was tied for the sixth-longest field goal in NFL history. Two of the five longer kicks, including Matt Prater’s record 64-yarder for the Broncos in 2014, were at high elevation in Denver.

Gostkowski added three field goals in the second half.

“We came a long way to win the football game,” Coach Bill Belichick said. “We came down here to win a game and that’s what we did. It was a great crowd tonight, a lot of energy, a great stadium and great environment. It was exciting to play here and coach here.”

Brady went 9 for 9 on the opening drive as the Patriots used an up-tempo offense and short passes to keep the Raiders on their heels. He capped it with a 15-yard pass to Dion Lewis to take a 7-0 lead.

Brady added a 5-yard TD pass to Amendola midway through the second quarter.

The Raiders appeared in position to score late in the first half before Marquis Flowers knocked the ball out of Seth Roberts’ hands inside the 5. Patrick Chung recovered with 33 seconds left at the New England 7. The Patriots moved 48 yards in four plays and ended the half with Gostkowski’s long kick. The Patriots have now scored in the final minute of the first half in seven straight games.

“That was a 10-point swing right there,” Raiders Coach Jack Del Rio said. “That was a tough one to swallow.”

Brady became the first quarterback with 300-yard games in three countries, having also done it twice in London and 79 times in the United States.