Montreal, who have won just seven of their last 47 games in Major League Soccer, took the lead in the 16th minute when Dominic Oduro broke down the right flank and his low cross was turned home by playmaker Ignacio Piatti.
America had a goal disallowed in the 26th minute when the dangerous Darwin Quintero put in Michael Arroya, who confidently slotted home but the linesman's flag was raised for offside.
The Mexicans were then lucky not to go down to 10 men just before the break when Osvaldo Martinez pulled down Oduro when the Ghanian forward was clean through on goal but he escaped with just a yellow card.
The Impact defended valiantly, with goalkeeper Evan Bush making a series of saves, but there was nothing he could do with a minute remaining when Peralta climbed over Calum Mallace to head in a floated free-kick from Rubens Sambueza.
America piled on the pressure in injury time with Martin Zuniga and Arroya both going close but the Canadian side held on for a result which they would certainly have settled for before the game.
With an away goal to their name Montreal will fancy their chances of becoming the first Canadian club to become CONCACAF champions, as well as the first Major League Soccer team to win the trophy since the current format was introduced in 2008.
(Reporting By Simon Evans; Editing by Peter Rutherford)
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