Real, from the Andean City of Cusco, advanced on penalties after losing Thursday's round of 16 second leg tie 1-0 in Montevideo for a 1-1 aggregate draw.
Gonzalo Bueno scored the only goal for the Uruguayans at the Centenario stadium, venue for the 1930 World Cup final, but despite constant pressure, they could not find a decisive second strike.
Former Inter Milan and Uruguay forward Alvaro Recoba then missed Nacional's first kick as they lost the shootout 4-1.
"We're a new team which people don't take much notice of," coach Freddy Garcia told Peruvian media. "But that type of adversity makes us better. We're a rebellious team."
Real Garcilaso were founded by former students of a local university in 2009. In their first full season, they won a district championship which earned them a place in the Copa Peru, a nationwide knockout tournament, for 2011.
That won that tournament as well to gain promotion to the 2012 national championship, where they eventually finished as runners-up to Sporting Cristal.
Clubs are started, wound up, renamed and relocated with bewildering speed in Peruvian football, which is beset by financial problems.
Real Garcilaso are one of four teams in the Peruvian top flight founded since 2000.
Universidad San Martin were founded by dentistry students in 2004, Sport Huancayo were created 2007 following the demise of Deportivo Wanka and Total Chalaco, initially known as Total Clean, were founded by a laundry in Arequipa in 2004.
Another side, Inti Gas, were renamed and re-located in 2008, having previously been known as Real Loreto and based in the Amazonian city of Iquitos.
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