Strikers Falcao, Alexis Sanchez and Edinson Cavani all scored as Colombia ate into Argentina's lead, Chile notched a second successive win and Uruguay revived their hopes in South American World Cup qualifying on Tuesday.
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Falcao's early penalty, taking his tally to seven in the competition, put Colombia on the road to a 2-0 home win over Peru that leaves them three points behind leaders Argentina with a game in hand.
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"Falcao was essential in the first half as Peru were unable to deal with his movement. He makes fantastic runs (off the ball)... the 'Tiger' is phenomenal," Colombia coach Jose Pekerman told reporters.
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Cavani struck a fine goal as Uruguay beat Venezuela 1-0 away for their first win in seven qualifiers, lifting the 2010 World Cup semifinalists up to fifth in the nine-nation group, which would earn them a playoff should they maintain the position.
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Uruguay leapfrogged Venezuela, a well-drilled outfit looking to take their country to the finals for the first time in Brazil next year, on goal difference with four matches remaining.
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"We were aware that it could have all been over for us today," Uruguay coach Oscar Tabarez, deprived of top scorer Luis Suarez through suspension, said.
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"We can't say the situation has got comfortable but it's an important step."
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Venezuela remain confident of qualifying, despite the setback.
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"We still have chances and I'm not going to surrender," coach Cesar Farias said.
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"We dominated the whole match but it's not about who deserves the win, it's about who scores the goals," captain Juan Arango added.
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Chile benefited from the revived goal instincts of Sanchez and the return after eight years of 33-year- old midfielder David Pizarro in a 3-1 home win over Bolivia that consolidated fourth place behind Ecuador on goal difference.
Uruguay as a country really know how to score goals when the time is right. They have gud strickers.