Peillat employed powerful flicks to the right of Germany goalkeeper Nicolas Jacobi in the ninth, 12th and 28th minutes in the first semi-final to help world No.7 Argentina reach the title clash for the first time.
Goals from Joaquin Menini (36th) and Lucas Vila (47th) minute ensured that the match became out of reach of world No.3 Germany, the second most successful team in Olympics men's hockey history.
Germany's desperation to make a strong comeback saw them score two goals in the final quarter. Captain Moritz Furste (51st) converted a penalty stroke, while Christopher Ruhr sounded the board in the 58th minute.
But Carlos Retegui-coached Argentina just needed to defend smartly as they had finished the match much before.
Germany, known for their discipline and structure, were caught at the turnovers as Argentine forwards Augustin Mazzilli and Vila pressed them higher, forcing the defence of the European team to make errors.
Defensive errors earned penalty corners for the Argentines and Peillat was up to the challenge. The 24-year-old former World Junior Player of the Year flicked past Jacobi thrice to give the 2014 World Cup bronze medallists a 3-0 lead till the half-time.
Even after the 10-minute break, the script didn't change for the Argentines. But the goal-scorers did. Menini jumped forward to meet a left cross from Mazzilli to make it 4-0 in the 36th minute.
Veteran forward Vila completed the drubbing with a clinical field goal to make it 5-0.
Later, Germany removed their goalkeeper to play with one extra outfield player and it helped provide the much needed thrust.
Furste, a leading figure of the 2008 and 2012 title winning sides, converted a penalty stroke. Later, Argentina managed to survive the pouring pressure exerted by the Germans.
Ruhr employed a backhand strike from the top left of the circle to beat veteran goalkeeper Juan Manuel Vivaldi, who had so far quelled every German effort.
Germany, coached by Valentine Altenburg, failed to find the third and conceded the defeat 2-5.
The hooter triggered wild celebrations in the Argentine camp, as former World Player of the Year Furste took a seat inside the goal, crestfallen to the core.
In the final, Argentina will meet the winner between Belgium and the previous edition's runners-up the Netherlands.
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