CONMEBOL World Cup qualifying wrap: Argentina held, Colombia prevail
Argentina were on track for their first defeat against Peru since 1997 but Real Madrid striker Higuain saved the visitors' blushes as they claimed a 1-1 draw in Lima.
The sides kicked off amid a frenzied atmosphere at the Estadio Nacional and Peru almost instantly had the chance to go ahead.
Schalke's Jefferson Farfan was brought down inside the penalty area just a minute into the match but Claudio Pizarro's resulting spot-kick was saved by Sergio Romero.
Peru finally got their goal 22 minutes into proceedings.
A well-worked set-piece found Luis Advincula alone on the right hand side and the full back crossed low into the area where Carlos Zambrano, slipping between two defenders, poked the ball home.
Argentina had failed to create any clear-cut changes with the first half drawing to a close but a swift counter proved why the South American giants are always a danger.
Federico Fernandez's long ball found Ezequiel Lavezzi in space and, with Peru pleading for an offside, the Paris Saint-Germain man crossed for Higuain to drive first time past Raul Fernandez and level the match.
Argentina remain atop of the CONMEBOL standings but Colombia closed the gap to just one point after they beat Chile 3-1, in a match which saw both teams reduced to 10 men.
Colombia, who trounced Uruguay 4-0 on Friday, came from behind to secure another valuable win in Monumental.
Despite going a man down in the 34th minute after Gary Medel received his marching orders for slapping defender Luis Perea, Chile hit the front five minutes later courtesy of a free-kick from Matias Fernandez.
The hosts went into half-time with a 1-0 lead but were made to pay for their numerical disadvantage in the final 45 minutes.
James Rodriguez, Radamel Falcao and Teofilo Gutierrez found the back of the net in a 20-minute period, while midfielder Abel Aguilar was sent off with three minutes left to play.
Elsewhere on Tuesday, Paraguay suffered their fourth consecutive loss after falling 2-0 at home to Venezuela.
Paraguay, the last-placed team in the South American qualifying zone, are on the brink of missing the World Cup for the first time since 1994 following a brace from Venezuelan striker Salomon Rondon.
Meanwhile, Edison Cavani cancelled out Felipe Caicedo's eighth-minute strike as Uruguay escaped with a point at home to Ecuador.