“This was important for me and for the team,” said Chile's Vargas. “It has boosted our confidence for the games to come.
“We are Copa America champions but we haven’t played as well as we did in the last Copa America and this will give us confidence.”
Chile went behind to an early goal but roared back thanks to outstanding performances from their front pair, who ran the Panamanian defence ragged.
Panama took the lead in the fourth minute after a mistake by Chilean goalkeeper Claudio Bravo, who let Miguel Camargo's shot from almost 30 yards squirm through his hands and into the net.
Chile fought back and were soon 2-1 up.
Artur Vidal and Sanchez worked a one-two in the box after 14 minutes and Sanchez's shot was only parried by Jaime Penedo and Vargas followed up to smash it home.
Three minutes before half time striker Vargas rose to glance home a header to put Chile ahead.
Sanchez was in captivating form and scored one of the goals of the tournament after 49 minutes.
Vargas was the provider this time, creating space for himself in the box before chipping to Sanchez, who volleyed home in spectacular fashion.
Panama kept fighting and pulled one back after 74 minutes and again Bravo was at fault, failing to stop Abdiel Arroyo's header from going in at his near post.
Sanchez had the last word, however, when he rose unmarked to head home a cross with two minutes left to make it 4-2.
In Seattle, few were expecting anything other than an Argentine win over already-eliminated Bolivia and most of the attention was focussed on whether Lionel Messi would surpass Gabriel Batistuta's record of 54 goals for his country.
Needing one to tie the mark, Messi came on as a second-half substitute with his team already 3-0 up through Erik Lamela, Ezequiel Lavezzi and Victor Cuesta.
The closest Messi came to scoring was from a free kick in the 61st minute but his curled effort sailed just wide.
(Writing by Andrew Downie, additional reporting by Jahmal Corner; Editing by Peter Rutherford)
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