Martin Palermo, the 36-year-old veteran, scored a last-gasp winner on 93 minutes after almost ten years in the international wilderness to send his nation one point above Uruguay into the fourth and final automatic qualification spot for next summerÃ¢â‚¬â„¢s tournament.
A win for Maradona was vital before their crunch clash away to Uruguay on Wednesday and, despite surprisingly omitting Sergio Aguero and Carlos Tevez in yet another controversial selection, his side began brightly.
Former Real Madrid and Manchester United defender Gabriel Heinze came close to opening the scoring in the sixth minute with a far post header that veered wide of the opposite corner.
Benfica star Angel Di Maria returned from a four-match suspension to hit a left-foot strike fizzing wide of the right-hand post after good work by Mascherano to win the ball and drive forward on 10 minutes.
Maradona finally conceded to the publicÃ¢â‚¬â„¢s clamouring for the selection of Real Madrid star Higuain by handing the 21-year-old his debut and the striker almost, and perhaps should have, repaid his faith on 19 minutes, but failed to convert Di MariaÃ¢â‚¬â„¢s pull back by firing a sliding effort over from close range.
He was presented with another chance moments later after be sent clear by the impressive Di MariaÃ¢â‚¬â„¢s beautifully weighted pass, but his scuffed shot was saved by the feet of Peru goalkeeper Leao Butron and held at a second attempt.
Pablo Aimar started his first game in an Argentine shirt for over two years in another of MaradonaÃ¢â‚¬â„¢s reshuffles and began to pull the strings alongside Messi in and around PeruÃ¢â‚¬â„¢s 18-yard box.
The Benfica playmaker came close on the half-hour mark with a cheeky backheeled effort just wide of the right-hand post following some intricate build-up play.
Action in a frustrating first-half of football for Argentina came to a close on 41 minutes with a viciousÃ‚Â strike hit with the outside of the left boot by Messi that veered just wide of the post.
Maradona needed to implement an attacking change for his side to take advantage of the numerous chances they were creating and the former Napoli superstar snubbed the talents of son-in-law Aguero and Man City striker Tevez in favour of Argentina-based Palermo at half time.
Peru began the second half on the front foot and forced a corner on 46 minutes. The corner-kick was pulled back by the ageing Nobby Solano for Juan Vargas to thump a volley crashing against the bar from all of 25 yards.
Argentina responded immediately by taking a much-needed lead three minutes later.
Higuain was sent through on goal by AimarÃ¢â‚¬â„¢s threaded pass to fire the ball right-footed past Butran and into the far bottom corner Ã¢â‚¬â€œ a debut-goal that was met by an immense wave of relief and celebration around the stadium.
But it was to be the calm before the storm, literally.
The hour mark was met with a downpour of driving rain and a chance for the away side to draw level after Johan Fano beat the Argentina offside-trap.
The striker, in acres of space, hit the ball into the body of the advancing Romero and the ball broke kindly for Solano to strike on the rebound, but his effort was blocked by an Argentine shirt with the goal gaping as Romero scrambled to get back into position.
Subsequent claims of an Argentina handball were waved away.
As weather conditions began to worsen, Maradona opted Ã¢â‚¬â€œ to the frustration of the home support Ã¢â‚¬â€œ for a more defensive approach by bringing on Di Michelis for goalscorer Higuain on 68 minutes.
His tactic backfired as his side lost their shape and invited Peru to apply pressure in the last quarter of the game.
Another defensive change saw Aimar replaced and Argentina continued to make hard work of bottom-placed Peru in increasingly difficult conditions.
Torrential rain and gale-force winds hammered down in what were an almost unplayable final few minutes in Buenos Aires and allowed Peru to sink Argentine hearts with a dramatic leveller.
Romero miraculously managed to get a foot to a flick-on from a pull back across goal but his defenders failed to clear their lines and the ball was chipped towards the far post from the right by-line and returned back over into the six-yard box for late substitute Hernan Rengifo to dart ahead of Romero and head into the net.
The rainfall continued to lash down onto the sodden turf and Argentina threw all they had into grabbing a winner and their reward came with only seconds to spare.
Di Maria crossed the ball back into the box following a clearance from a corner-kick and it was driven back towards the back post where Palermo was on hand to prod the ball home and send his coach sliding on his front along the rain-soaked touchline in truly jubilant scenes.
Peru struck the crossbar from kick-off in an audacious attempt to equalize for a second time with the last kick of the game but it couldnÃ¢â‚¬â„¢t prevent the frenzied celebrations at the sound of the final whistle.
Victory over Uruguay at the Estadio Centenario on Wednesday evening and Maradona and his side will be celebrating booking their place in South Africa. A feat that fans of football across the globe will hope they achieve.
Argentina: Romero, Gutierrez, Schiavi, Heinze, E Insua, Mascherano, Perez (Palermo, 45), Di Maria, Aimar (F Insua, 76), Messi, Higuain (Di Michelis, 68)
Peru: Butron, Zambrano, Rodriguez, Prado, Vilchez, Solano (Palacios, 65), Torres, Vargas, Ballon, Ramirez, Fano (Rengifo, 72)
Man of the Match: Martin Palermo Ã¢â‚¬â€œ Returned from a 10-year international absence to win all three desperately-needed points at the death.
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