Argentina started slowly and could have fallen behind in the third minute when the hosts were awarded a penalty. Angel di Maria fouled Jefferson Farfan but goalkeeper Sergio Romero saved Claudio Pizarro's spot-kick to keep the scores level.
The visitors continued to look subdued, particularly talismanic forward Lionel Messi, and Peru took a deserved lead in the 22nd minute when defender Carlos Zambrano slotted home Farfan's low cross from the right.
Seven minutes before halftime Argentina equalised with their first meaningful attack, Higuain applying a superb finish to Ezequiel Lavezzi's cross to register his sixth goal of the qualifiers.
Despite the draw, Argentina remain top of the South American standings on 14 points from seven matches, one ahead of Colombia and Ecuador, and two in front of Uruguay and Chile. Peru have seven points.
Argentina coach Alejandro Sabella said the state of the pitch, hard and with long grass, prevented his team from developing the fast attacks that had brought them three qualifying wins in a row scoring nine goals.
The visitors were outplayed for large passages and were unable to bring Messi into the game due to Peru's close man-marking system.
"The tactic of playing with three forwards means our rivals can often have the ball more than us, the thing is to hurt them when we have it," he told a news conference.
Messi told reporters he was disappointed that Argentina could not play their game, saying: "It was more fight than football, we couldn't play as we like.
"Higuain's goal was worth a lot. We got a draw which isn't bad in the qualifiers," he added.
PERU HIT POST
Argentina's Lavezzi forced Raul Fernandez into a diving save early in the second half, and at the other end of the pitch Peru's Luis Ramirez hit the post.
Fernando Gago was badly injured after 60 minutes when a Peruvian defender fouled the Argentina midfielder then fell on top of him.
Gago was carried off on a stretcher with a neck brace and taken to hospital, with Pablo Guinazu taking his place. Gago suffered concussion but soon recovered, according to Argentina media reports.
Peru's Pizarro missed another golden chance when he had a free header after his marker fell over in the box but his effort went wide.
Higuain almost snatched what would have been an undeserved winner for Argentina in added time with a low shot that Fernandez pushed out for a corner.
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