Mexico defeated Uruguay 3-1 in a stormy Copa America Centenario that saw both teams finish with 10 men after a pre-match furore over a bungled national anthem.

A pulsating clash at the University of Phoenix stadium in Arizona saw Mexico take all three points in the crucial Group C battle through an own goal from Alvaro Pereira and late strikes from Rafa Marquez and Hector Herrera.

Uruguay's lone strike came from captain Diego Godin, the Atletico Madrid player heading in an equalizer 16 minutes from time that looked to have secured the South Americans a share of the points.

But 37-year-old Marquez's emphatic strike into the roof of the net on 85 minutes fired Mexico 2-1 up before Herrera added a third in injury time to complete a memorable victory for "El Tri".

Uruguay's players angrily remonstrated with match officials at the final whistle in an ill-tempered finale that capped a miserable afternoon for 'La Celeste'.

Before kick-off, Uruguay's players had looked baffled as they lined up for their national anthem -- only for Chile's national anthem to be played by mistake.

Copa America Centenario organizers swiftly apologized for the blunder.

"We sincerely apologize to the Uruguayan Federation, the Uruguay National Team, the people of Uruguay and to the fans for this mistake," a statement said, blaming the gaffe on "human error."

When the game kicked off, Mexico took the lead after only four minutes with a goal that owed everything to the guile of PSV Eindhoven midfielder Andres Guardado.

The 29-year-old wide player carved out space for himself on the left flank superbly and then whipped in a wicked cross that sowed panic in the Uruguayan defense as Herrera lurked menacingly.

Alvaro Pereira spotted the danger but as he scrambled to neutralize the threat, succeeded only in powering a header into his own net.

Godin pelted

The goal rocked Uruguay who struggled to find their rhythm in the early exchanges.

Paris Saint-Germain striker Edinson Cavani almost went close to equalizing on the half hour, but his low shot was saved brilliantly by Alfredo Talavera in the Mexico goal.

On the stroke of half time it got worse for Uruguay when Matias Vecino picked up a second yellow card and received his marching orders.

Diego Rolan almost equalized after a superb charging run from his own half by Godin, who laid off to Cavani who fed Rolan, only for the Uruguayan to shoot wide.

Before kick-off, Uruguay's players looked baffled as Chile's national anthem was played by mistake. Photo: AFP

Guardado then received a second yellow to earn a red card and from the ensuing free-kick Godin headed Uruguay level -- before being pelted with missiles from the overwhelmingly pro-Mexico crowd as he celebrated.

The game appeared headed for a draw but Marquez rifled home score his 16th international goal in 131 appearances to put Mexico 2-1 up and Herrera added his injury-time third.

Uruguay's veteran coach Oscar Tabarez refused to be downcast in defeat, paying tribute to his side's "courage" in coming back to level in hostile conditions.

"I'm proud of the courage of the team and the way we came back," said Tabarez, whose side now face a tricky second game against Venezuela in Philadelphia on Thursday. Venezuela improved their chances of progressing with a 1-0 win over Jamaica earlier Sunday.

"We are in a difficult situation with Venezuela," Tabarez said.

"We have to try to play well in that game, because if we lose we are out of the Cup," he said.

Venezuela defeated Jamaica in Chicago thanks to a 16th minute strike from Josef Martinez.

Jamaica were reduced to 10 men after Rodolph Austin was sent off in the first half while coach Winfried Schaefer was also banished from the dugout at halftime.