The Fiorentina winger, who starred and scored in his country's Copa America quarter-final win, put the extra-time victory down to a superb team spirit in the camp
With the match scoreless after 90 minutes of football, extra-time was required. Peru punished Porto striker Falcao for his penalty miss in normal time as they scored twice, courtesy of Carlos Lobaton and Vargas himself.
"This group was very united on the pitch. Now we have another, more important game (in the semi-finals) and we have four days to work at it and maintain what we have at the moment," he was quoted as saying by Goal.com after the match.
"My goal came as a result of the work I put in on the pitch. But for me the important thing is to score the goal and help the team win."
Vargas' coach Sergio Markarian echoed the thoughts of the Fiorentina man and admitted it will be an uphill struggle to lift his players for another big push in the next round.
"It is vital that we do everything we can from now until the semi-final. It will be difficult to recover. But the squad is united and this is critical. I have 22 players and none of them complained whether they played or not.
"We have good players. Before, it was said that we play nice football but I have strived to make the team more efficient. Sometimes, you have to sacrifice style for substance."
Peru will take on either Argentina or Uruguay in the semi-final on July 19.