James Rodriguez scored a goal and set up another in the first 30 minutes, and Colombia clinched a berth in the Copa America quarterfinals with a 2-1 victory over Paraguay on Tuesday night.

Colombia became the first team to secure advancement to the knockout stage of the tournament with stellar goaltending from David Ospina and another dynamic performance from Rodriguez, who shook off a shoulder injury that made his availability a game-time decision at the Rose Bowl.

The Real Madrid midfielder propelled Colombia to its second win in two matches, following a 2-0 victory over the United States last week.

Victor Ayala scored Paraguay's first goal of the Copa America in the 71st minute on a long shot past Ospina, who made a handful of jaw-dropping saves to keep Colombia ahead.

Despite a few defensive struggles, the world's third-ranked team has lived up to its billing so far stateside with a fluid, attacking game built around Rodriguez, who played despite hurting his shoulder last week.

Carlos Bacca scored on a header from Rodriguez's corner kick in the 12th minute. Rodriguez then scored with an exceptional shot after a long scramble in the box in the 30th minute. Colombia missed on several chances to score in a back-and-forth second half, while Ospina stopped everything except Ayala's exceptional long strike.

Los Cafeteros wrap up group play against Costa Rica in Houston on Saturday, while Paraguay travels to Philadelphia to face the Americans. Paraguay must beat the home team to stay in contention for advancement.

Paraguay tested Colombia's defense throughout an entertaining game, but La Albirroja don't have a player with the skills of Rodriguez — or the goaltending reflexes of James' brother-in-law, Ospina.

After Bacca put Colombia ahead with another goal in his strong run of recent play, Rodriguez showed off his skill with his team-leading 16th goal for Los Cafeteros. Surrounded by defenders, Edwin Cardona tipped the ball outside to the charging star, and Rodriguez slotted a pinpoint shot into the far corner of the net.

Ospina, the Arsenal backup, made a fingertip save in first-half injury time to deflect Dario Lezcano's short free kick off the crossbar. He was even better in the second half with a flying, one-handed deflection of a header in traffic.

But Ospina could do nothing against Ayala, who trimmed Colombia's lead and made the final minutes uncomfortable.

Paraguay's task became tougher when Oscar Romero was sent off in the 81st minute, getting his second yellow card in three minutes after a defensive sequence in which he pulled roughly on Rodriguez's jersey and wrapped both arms around Guillermo Celis.

The Rose Bowl crowd of 42,766 was dominated by yellow-clad fans from Los Angeles' vibrant Colombian community and beyond. They gathered in Arroyo Seco several hours before kickoff for food, music and a celebration of a serious championship-contending team.

The fans stood and cheered when Clint Dempsey headed off the field in the second half, and the forward responded with his own round of applause.

Brad Guzan held his arms in the air after the final seconds of his happy homecoming.

After days of questions and criticism, it was a couple of perfect pictures for the United States.

Dempsey had a goal and two assists, and the U.S. rebounded from its opening loss in Copa America with a convincing 4-0 victory over Costa Rica on Tuesday night.

"Goals change games, and the guys up front took care of that," said Guzan, who only had to make one save in his 16th international shutout.

Dempsey, Jermaine Jones and Bobby Wood scored in the first half and substitute Graham Zusi added another goal in the 87th minute as the U.S. moved into prime position to grab one of two spots in the knockout round coming out of Group A in South America's championship.

A victory against Paraguay on Saturday night in Philadelphia and the Americans are through to the next stage.

It was quite a response to days of questions after the U.S. allowed a goal off a corner kick and committed a costly hand ball in a 2-0 loss to Colombia on Friday night. Another loss against Costa Rica and the U.S. would have been eliminated on the fifth day of the tournament.

"I see a team progressing. I see a team that badly wants to prove itself with these caliber teams in the Copa America," U.S. coach Jurgen Klinsmann said.

"It was a very, very encouraging performance by us against Colombia. Obviously, the result, especially here in the U.S., that's all that matters to a lot of people. ... The team, they know where they stand."

Costa Rica, which played a scoreless tie against Paraguay in its Copa opener on Saturday in Florida, looked sluggish for long stretches of the first half and was unable to recover. It played without key defender Kendall Waston after he got a red card in the previous game.

The loss to Colombia ramped up criticism of Klinsmann, who said last month the Copa goal for the Americans was the semifinals.

U.S. Soccer Federation President Sunil Gulati told a group of reporters before the match that recent results for the men's team "haven't been what we would have hoped for, especially in the official competitions."

But Klinsmann and his players insisted they felt pretty good in the team's performance on Friday night in Northern California, and the coach doubled down on the positive vibe by sending out the same starters against defensive-minded Costa Rica.

And it worked - in a big way.

Moments after DeAndre Yedlin's poor clearing attempt almost set up an early goal for Costa Rica's Joel Campbell, the Americans started to find their way.

Wood was pushed in the back by Cristian Gamboa when he attempted to go after a cross into the box, drawing a penalty kick despite a series of protests in front of referee Roddy Zambrano. Dempsey then drove it past Patrick Pemberton on the goaltender's left side for a 1-0 lead in the ninth minute.

It was Dempsey's 50th international goal. He also scored his first at the home of the NFL's Chicago Bears on May 28, 2005, against England.

"You know where you kind of are in terms of the goals you've scored for the team," Dempsey said. "Yeah, it's good to be part of that club of getting to 50 goals. But the most important thing is we got the win tonight."

The United States seemed to get stronger as the first half went along, and an alignment change to four midfielders helped fuel another flourish in the final minutes.

Jones stole the ball at midfield and passed to Dempsey, who carried it deep into the Costa Rica side. The forward then nudged it back over to Jones, who shot it on the ground past a diving Pemberton in the 37th minute.

With Costa Rica looking a little ragged, the U.S. kept up the attack. Dempsey passed to Wood in the middle, and he turned away from defender Oscar Duarte before beating Pemberton on the ground for a 3-0 lead in the 42nd minute - delighting the crowd of 39,642 that filled most of the lower bowls on a cool, cloudy night in Chicago, but left wide swaths of empty seats in parts of the stadium.

Guzan, playing near his hometown of Homer Glen, Illinois, clapped as he headed off the field after the halftime whistle, and Costa Rica barely challenged in the second half. Midfielder Bryan Ruiz sent a header off the left post in the 67th minute on the Ticos' best opportunity of the night.

"I think it was, overall, a very, very pleasant performance," Klinsmann said. "It confirms the spirit of the group. The spirit is excellent. They're there for each other. The whole bench is jumping up and down. Everybody wants the other one to do well. It's a good group of guys we have together."