Colombia became the first side to reach the quarter-finals of the Copa America Centenario, while the United States thumped Costa Rica 4-0 to get their campaign back on track.
Goals from AC Milan's Carlos Bacca and Real Madrid star James Rodriguez on Tuesday secured a 2-1 win for Colombia over Paraguay in front of a vocal crowd at the Pasadena Rose Bowl in California.
Victor Ayala gave Paraguay hope after pulling a goal back on 71 minutes but Colombia held on for three points which means they are assured of a top two finish in Group A and a place in the last eight.
Colombia need only to draw against Costa Rica on Saturday to assure themselves of first place, leaving them a potentially easier quarter-final against the runner-up from Group B, which contains Brazil, Ecuador, Haiti and Peru.
In Tuesday's other game, US striker Clint Dempsey scored his 50th international goal as the host nation bounced back from their 2-0 loss to Colombia on Friday with a convincing rout of Costa Rica.
Dempsey opened the scoring from the penalty spot after nine minutes before Jermaine Jones and Bobby Wood struck just before half-time to effectively settle the contest.
Substitute Graham Zusi added a fourth goal three minutes from time, which could prove crucial if goal difference comes into play.
The win came as a welcome relief for US coach Jurgen Klinsmann, whose tenure has faced mounting criticism over the past 18 months after a series of disappointing performances in competitive matches.
United States Soccer Federation chief Sunil Gulati had fueled fresh speculation about Klinsmann's position only hours before kickoff, telling journalists: "No one has iron-clad job security."
Klinsmann meanwhile showed he was in no mood to cede ground to his critics, picking the same starting line-up to face Costa Rica that had disappointed in the 2-0 defeat to Colombia.
Klinsmann's faith was rewarded with a superb first half display from his team.
"I think it was, overall, a very pleasant performance," Klinsmann said.
"It confirms the spirit of the group. They are all there for each other, the whole bench is jumping up and down when we score. Everybody wants the others to do well. It's a good group of guys that we have together.
"They deserve a huge, huge compliment for tonight's performance.
"We were eager to get on the field, eager to get our first three points of the tournament.
"We took a bit to get into the game. But when the first goal came we kept pushing for the next one and the next one."
Klinsmann's team now faces Paraguay in its final Group A game in Philadelphia on Saturday, where a draw will probably be enough to advance to the knockout rounds.
"We wanted to put ourselves in the driving seat against Paraguay and that's what we did," Klinsmann said.
"We are right there to get through a difficult group, and this is the most difficult group in the Copa America. It's encouraging to see this group of players has the extreme hunger to make things happen."
On Wednesday, Peru could join Colombia in the quarter-finals if they manage to defeat Ecuador in Glendale, Arizona in Group B.
In Wednesday's other game, five-time world champions Brazil face an intriguing matchup against Caribbean minnows Haiti in Orlando, Florida.
"If we win it will be the greatest miracle that God has produced in football," Haiti midfielder Jean-Marc Alexandre said Tuesday.