LIMA - Alexis Sanchez scored the first goal and contributed to the other two as he inspired Chile to a 3-1 win away to arch-rivals Peru in a World Cup qualifier on Sunday. The 21-year-old Udinese forward also suffered the foul which led to Peru's Juan Vargas being given a red card in the 53rd minute for a second bookable offence. The win lifted Chile into third place in the 10-team South American group with 19 points from 11 games, behind Argentina on goal difference and one ahead of Brazil who drew 1-1 with Ecuador. Paraguay lead with 23 points. Peru, lucky not to have more players dismissed for some wild tackling and incapable of stringing more than a couple of passes together, stayed bottom of the group with seven points after another dire performance. The top four teams qualify for South Africa in 2010 and the fifth plays off against the fourth side from the CONCACAF zone for another place. Chile ignored a hostile reception at the Monumental stadium as Sanchez volleyed them ahead from Mark Gonzalez's cross after two minutes. In the 32nd minute, Sanchez was upended by Vargas and Humberto Suazo fired home the resulting penalty. Johan Fano pulled one back two minutes later but Vargas's dismissal ended any remaining hopes of a Peruvian fightback. Chile continued to attack in numbers, a hallmark of their enigmatic Argentine coach Marcelo Bielsa, and settled the game in the 72nd minute. Suazo found Sanchez on the right and he pulled the ball back for Matias Fernandez to score into an empty net after a swift counter-attack. Peru, who last qualified for the World Cup in 1982 when they were a dominant force in South America, are almost certain to miss out again and were left contemplating a four-year wait before they can have another try.