Teenage sensation Renato Sanches, who scored Portugal's goal and smashed home one of the penalties, said it was a "wonderful moment for the team and for me for scoring".
Portugal have reached the last four without winning a single game within 90 minutes.
"People criticise us but we don't care, because we are in the semis," Sanches said, after Portugal reached the semi-finals for the fourth time in the last five European Championships.
Goalkeeper Rui Patricio and Ricardo Quaresma were Portugal's heroes in the shootout. Ronaldo was among the players fist-pumping when Patricio dived to his left to save Jakub Blaszczykowski's tame fourth shot for the Poles, who had reached the quarter-finals for the first time.
Quaresma was next up for Portugal and made no mistake firing high into the net to beat Poland goalkeeper Lukasz Fabianski.
Poland made a blistering start to the game. After barely 100 seconds, Kamil Grosicki hurried past Southampton right-back Cedric Soares to deliver a great cross that Lewandowski drove past a flailing Rui Patricio at his near post.
The Polish striker's first goal of the competition, after hitting a record 13 in qualifying, stunned Portugal. The early goal gave Poland momentum, and a defiant but borderline interception by Grzegorz Krychowiak on Sanches set Arkadiusz Milik up for a 25-yard drive that sailed wide on the quarter hour.
German referee Felix Brych waved away Ronaldo's claims for a penalty on 31 minutes despite replays suggesting the Real Madrid star was bundled over by centre-back Michal Pazdan as he went to meet a cross.
