Federico Bernardeschi netted the only goal of the game 30 minutes in to lift the Azzurrini from third place to top, while their opponents had already done enough in their two previous games to go through as the best-placed runners-up.
Record five-time winners Italy will now take on tournament favourites Spain in the semi-finals, and there is a repeat of the 2009 final in the other as Germany entertain England next week.
Italy looked the more lively in the opening stages in Krakow but it is Germany who should have taken the lead, finding the back of the net through a powerful Marc-Oliver Kempf header that was wrongly ruled out for offside.
Italy were beginning to up the pressure as the first half wore on, coming close through a Bernardeschi free kick and then getting their reward right on the half-hour mark.
It was Bernardeschi who bagged it, picking his spot past Pollersbeck after profiting from some slack play from the Germans as they tried - and failed - to pass the ball out from the back when outnumbered.
Things boiled over in the aftermath of the goal, leading to yellow cards being shown to Domenico Berardi and Maximilian Arnold - two of six players to be cautioned in a tense first half of a game that had plenty riding on it.
Italy's lead did not come under any real threat until the hour mark, when Germany finally managed to turn the screw a little, yet it was the Azzurrini who looked the more likely to score at that point as Pellegrini was denied by Pollersbeck from the edge of the box.
Chances were proving to be very limited in a disappointing second half, with the scoreline remaining enough to see both sides through thanks to results elsewhere.
Conti squandered a half-decent opening at the back post as the final 10 minutes approached, although the offside flag went up regardless, and that proved to be it as the sides simply failed to show any attacking impetus and allowed the game to peter out.