Mexican champions Tijuana started their Copa Libertadores Group Five campaign with a 1-0 away win over Millonarios in Colombia, their first in the competition.
Richard Ruiz netted the winner in the 61st minute after an Edgar Castillo cross, while Millonarios defender Roman Torres was sent off in the last minute of the game.
Olimpia produced a fine performance to defeat Universidad de Chile 3-0 to get their Group Seven campaign going.
Two goals in the first 10 minutes of the match ensured the Paraguayan side would be celebrating at the final whistle.
Uruguayan striker Juan-Manuel Salgueiro put Olimpia ahead after just 75 seconds with a long-range strike and in the eighth minute Richard Ortiz headed home to make it two.
Three minutes after the interval, defender Salustiano Candia cashed in on a defensive mistake by Paulo Magalhaes to make it 3-0.
Magalhaes was then sent-off after 69 minutes for elbowing Ortiz.
Olimpia had suffered a 3-1 defeat at Newell's Old Boys last week.
"We played well tonight. In the last few minutes we felt a little tired because we pressured a lot in the opening minutes but I'm glad for my team," coach Ever Almeida told reporters.
"We scored very quickly and that shocked the rivals. This is a great result for Olimpia."
Uruguay's Penarol took control Group 4 with six points from two games as they saw off Ecuador's Emelec 1-0.
In the 67th minute, Fabian Estoyanoff crossed the ball and Juan-Manuel Olivera despatched the ball into the back of the net.
Elsewhere, Vicente Sanchez scored a brace against former club Toluca as Nacional claimed an important 3-2 win.
Former Toluca midfielder Sanchez did not celebrate any his strikes as Nacional twice came from behind.
Panamanian forward Luis Tejada gave Toluca the lead in the 21st minute, but Sanchez equalised two minutes after the break.
Edgar Benitez put Toluca ahead again at the 51st but the lead did not last too long as Sanchez levelled again three minutes later.
Ivan Alonso then finished a Juan-Angel Albin assist in the 56th minute to put Nacional on top of Group One with four points, while Toluca stayed on three.
Information from the Press Association was used in this report.