The victory keeps alive Argentina's hopes of qualifying for the 2010 finals in South Africa as they climbed into fourth place in the South American group before their last qualifier away to Uruguay on Wednesday.
The top four go through automatically with Uruguay, a point behind Argentina, perched in the fifth-place play-off berth after beating Ecuador, who are now in sixth another point back.
New cap Gonzalo Higuain put Argentina ahead two minutes into the second half from Pablo Aimar's through ball and, as driving rain became steadily worse at the Monumental, Peru equalised in the final minute through substitute Hernan Rengifo.
But Palermo had the last word when he turned in a deflected shot from the right by fellow substitute Federico Insua in a packed area as Argentina threw everything at their opponents in search of the winner.
"I told him at half-time 'go and resolve this'," coach Diego Maradona told reporters. "It was a miracle from Saint Palermo that gives us another life."
It was the 35-year-old's third goal in two internationals after scoring two in a friendly against Ghana on Sept. 30.
Peru would not have been unworthy of a draw, giving a second-half performance that belied their position at the bottom of the group and out of the finals.
"Perhaps with less pressure I imagine Argentina will show more than what they showed today," coach Jose del Solar said.
SEVERAL SCARES
Argentina, dominant in the first half, were constantly under threat in the second as Peru, having fallen behind, fought for an equaliser, snatching the initiative for long spells.
One minute into the second half, defender Juan Manuel Vargas volleyed from 25 metres and keeper Sergio Romero managed to tip the ball onto the bar and over.
They had another scare right after Higuain's goal when Romero blocked Johan Fano's shot and the rebound fell to Luis Ramirez only for left back Emiliano Insua to block with his body. The referee waved away Peru's claims for a penalty.
Argentina had yet another scare when Peru broke on the right and a shot went across the face of goal with home defender Rolando Schiavi managing to deflect it wide of the far post.
In the first half, with Lionel Messi marked tightly on the right of the attack, Argentina were more dangerous on the left flank with Angel Di Maria, back from suspension, giving defender Amilton Prado a torrid time and linking well with Higuain.
Twice in the space of two minutes midway through the half Higuain was close to beating keeper Leao Butron at the near post from low crosses by Di Maria.
Messi was close with a free kick and a shot that skimmed the top of Butron's goal but whenever he tried to weave his way through the massed Peruvian defence he made little headway.
