Euro 2012: Poland 0 Czech Republic 1
Poland, the tournament co-hosts, were knocked out with their defeat in the team's final Group A game.
The Czechs finished top of their group and will now play the runners-up in Group B.
Pushing forward in the 72nd minute, Jiracek collected a pass from Milan Baros in the box, cut right to clear past Poland's Marcin Wasilewski and slotted the ball inside the far post.
"We had a poor start but we gradually improved, started to create chances and finally, we deserved to score," Jiracek said.
Poland, who had to win to advance to the quarter finals, immediately brought on two attacking players in the last 30 minutes to push for a goal but couldn't punch through the Czech defense.
After the final whistle, the Czech players swarmed around each other on the pitch. The Poles fell to the ground, covering their faces.
"I think that probably we were too sure about winning this game. The Czechs played excellent football," Poland coach Franciszek Smuda said. "We had some opportunities before halftime, we didn't take advantage of them and we lost the game."
The Czechs pulled off the win despite playing without their captain and playmaker Tomas Rosicky, who was sidelined with an Achilles tendon injury.
Without his creative skills the Czechs were listless in the first half, struggling to put together any fluid passing and reduced to knocking long balls forward.
But as the Poles pushed forward in the second half in search of a goal to put them through to the quarterfinals, more space began to open up in midfield.
That space gave the Czechs the opportunity to strike on the counter, and the punishment came with Jiracek's second goal of the tournament. He also scored in the Czechs' 2-1 over Greece on Tuesday.
Poland responded well, though, and the final chances were all for the home team.
A cross from the right was deflected to the far post, where Marcin Wasilewski met the ball with a header that just cleared the bar. Minutes later, Poland captain Jakub Blaszczykowski's angled effort was cleared off the line by Michal Kadlec as the Czechs sealed their place in the last eight.
"In the first half we had some chances and didn't take advantage of them," Blaszczykowski said. "With the time passing, we had to open up more and more, and I think this is the reason we conceded a goal on the counter."