It was also an unhappy 100th Poland appearance for Robert Lewandowski, who barely had a touch of the ball.
After two games Portugal top the group with six points, while Poland and Italy have one apiece.
Portugal, who are rebuilding their team after a second-round exit at the World Cup, left out a number of old favourites including Joao Moutinho, Jose Fonte and Ricardo Quaresma.
Captain and alltime leading scorer Cristiano Ronaldo was also absent by what coach Fernando Santos said was mutual consent, although he is expected to be recalled next year.
Piatek, scorer of nine goals in seven Serie A matches for Genoa this season, struck an early blow when he outjumped Joao Cancelo at the far post to head Poland in front from a corner in the 18th minute.
But after that, it was mainly one-way traffic as Portugal took control.
Andre Silva levelled in the 31st minute, turning in Pizzi's low cross following a well-worked move down the right for his 14th goal in 29 appearances.
Ruben Neves set up the second with a majestic long ball from inside his own half which caught out the Polish defence.
Rafa Silva got on the end of it and his first touch took him past goalkeeper Lukasz Fabianski before Glik put the ball into his own net.
Seven minutes after halftime, Bernardo Silva collected the ball near the touchline, jinked inside one marker, ran across the edge of the penalty area and scored with a low shot past Fabianski.
Portugal continued to dominate even after Blaszczykowski's goal and Renato Sanches was twice close to a fourth for the visitors.
(Reporting by Brian Homewood; editing by Ken Ferris and Toby Davis)
