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 half-time 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 said.
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.
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.
Strikers Radamel Falcao and Teo Gutierrez confirmed their red-hot scoring form as Colombia came from a goal down to beat 10-man Chile 3-1 at the Monumental.
Colombia, who crushed Uruguay 4-0 at home on Friday, joined Argentina at the top of the South American group on 13 points, at least until Lionel Messi's side meet Peru in Lima later on Tuesday.
The hosts nevertheless took the lead five minutes before the interval with a fine free kick from playmaker Matias Fernandez.
Goalkeeper Claudio Bravo then kept Chile in the match with a string of fine saves although he was helpless with midfielder James Rodriguez's free kick equaliser just before the hour which went in off his left-hand post.
Colombia's Argentine coach Jose Pekerman, appointed late last year and instrumental in their recovery from a poor start to the qualifiers, made a telling substitution in midfield in the 73rd minute, bringing on Aldo Ramirez for Macnelly Torres.
Ramirez had an immediate impact with a fine through ball to Falcao who steered it past Bravo to put Colombia ahead in the 74th with his third goal in two games.
Gutierrez, who like Falcao had scored twice against Uruguay, increased the visitors' lead three minutes later when he took a pass from his strike partner on the left and beat Bravo with a low shot inside the near post.
Colombia midfielder Abel Aguilar was sent off three minutes from time for handball, his second booking.
"We got three points that take us nearer to what we want.
Chile had a very good first half but we were able to come back and we finished very well," Pekerman told Fox Sports.
"This is thanks to my family, my personal trainer and my psychologist so that I could do things properly," said the mercurial Gutierrez, recalled by Pekerman following a troubled spell at Racing Club in Argentina.
"We have a good understanding (with Falcao), this is a very nice family," he added referring to the Colombia squad.
"Pekerman has given us a lot in the tactical aspect and in the mental aspect," Rodriguez said.
Striker Edinson Cavani hit a 67th minute equaliser to give South American champions Uruguay a 1-1 draw with Ecuador at the Centenario and save them from a second successive defeat in the World Cup qualifiers.
The Uruguayans, whose 18-match unbeaten run came to an end with a 4-0 loss in Colombia on Friday, have dropped down the South American standings and are one point behind Colombia, Ecuador and leaders Argentina, who faced Peru later on Tuesday.
Cavani secured a point for Uruguay when the ball was poorly cleared from an attack down the left and ran loose to the striker on the right, from where he shot left-footed low into the bottom of the far corner.
"Their goal woke us up, we began to put more intensity into our game and it was like that right to the end, that's why we managed to draw," Cavani told reporters.
"I think they had the luck to find (an equaliser) when there were two rebounds as we tried twice to clear (the ball)," Ecuador's Colombian coach Reinaldo Rueda said.
Ecuador, who were in control for long spells and especially in the first half, were stunned when they were denied a penalty by Paraguayan referee Carlos Amarilla just past the hour when they were still a goal ahead.
Uruguay goalkeeper Fernando Muslera appeared to trip Cristian Benitez with his outstretched leg as the striker tried to run past him in a solo breakaway but instead Amarilla booked the Ecuadorean for diving.
Striker Luis Suarez might have equalised in the 43rd minute but his shot hit the bar and he was denied a winner two minutes from time when his header was saved by Alexander Dominguez.
Ecuador winger Antonio Valencia was sent off in the fourth minute of added time after a second booking for obstruction.
Striker Salomon Rondon scored twice to give Venezuela a 2-0 away win over Paraguay in the Defensores del Chaco cauldron.
Venezuela, looking to reach their first World Cup finals, have left 2010 quarter-finalists Paraguay with very little chance of making it to their fourth tournament in a row in Brazil in 2014.
The Venezuelans have 11 points from eight matches while Paraguay are bottom of the nine-nation standings with four.
Rondon latched onto a perfectly weighted pass from midfielder Cesar Gonzalez to score from the right on the stroke of half-time and set Venezuela on their way to their first win in a qualifier in Asuncion.
The striker scored again in the 68th when Paraguay keeper Justo Villar punched a free kick in his six-yard box and the ball came back off defender Paulo da Silva to Rondon who steered it into the net.
Venezuela's young goalkeeper Daniel Hernandez played his part in the victory with good saves from Oscar Cardozo, who also hit the post early in the match, Jonathan Fabbro and Nelson Haedo Valdez.