Del Piero (left) and Grosso scored to put Italy into the final
An absorbing semi-final seemed set for penalties until Grosso curled man of the match Andrea Pirlo's pass past Jens Lehmann with just one minute left.
Del Piero then finished an Italy break with a delicate chip into the corner.
Germany's Lukas Podolski earlier sent a header wide and saw a shot saved, but the hosts' Cup dreams were shattered.
There were, unsurprisingly, tears among German players and fans after the extraordinary end to an enthralling encounter - in which Italy also hit the woodwork twice in extra-time.
The opening 90 minutes were intriguing - but goalless - and it was in the extra period that the game truly exploded into life.
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The Italians, famed for their defensive strength, adopted an increasingly attacking approach, aware of the Germans' brilliant record at penalty shoot-outs.
Substitute Alberto Gilardino's shot rebounded off the post and Gianluca Zambrotta's drive struck the bar.
But Podolski led the German attacking threat, missing the header from David Odonkor's cross and forcing a brilliant one-handed save from Gianluigi Buffon.
Del Piero then squandered a shooting chance from the edge of the box after great work from Vincenzo Iaquinta and Francesco Totti and Pirlo forced a diving save from Lehmann.
Jurgen Klinsmann was left in despair by Italy's late goals
But Pirlo still had time to have his say as, with Italy pushing forward in numbers, he threaded the ball to Grosso whose first-time shot left Lehmann with no chance.
The goal was timed at 119 minutes and Germany, and their supporters who had crammed into Dortmund's Signal Iduna Park, were stunned.
And as Jurgen Klinsmann's side pushed forward in desperation, Gilardino found the ball in space and rolled it to Del Piero who sent a clinical finish beyond the advancing Lehmann into the roof of the net.
The opening 90 minutes saw Italy work the first clear opening as Totti's astute pass picked out Simone Perrotta, but Lehmann smothered the ball.
Fabio Cannavaro, exceptional throughout the match, marshalled the Italian back line effectively and limited Germany in the opening period.
Italy saw a Pirlo free-kick on 24 minutes elude both Luca Toni and Marco Materazzi by a fraction.
606 VIEW Italy deserved it, Cannavaro was at his very best
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Then Toni was played in by Grosso, only for his goalbound shot to be blocked by Per Mertesacker.
Germany, however, fashioned the best chance of the first half, but Bernd Schnieder shot over after finding rare space behind the Italian defence.
Buffon had to make his first real save, and had to race from his goal to block as Miroslav Klose danced his way into the area.
Germany were on top and Buffon parried a close-range effort from Podolski 12 minutes later.
But extra-time seemed inevitable as Michael Ballack, not at his imperious best, sent a free-kick over the top from 20 yards.
Indeed, the 90 minutes ended without a goal - opening the dramatic extra period in which Grosso and Del Piero wrote themselves into Italian football history.
Their delight at the final whistle was in stark contrast to Germany, who were left bereft as their dream of lifting the World Cup on home soil came to a sudden, heart-breaking end.
Germany: Lehmann, Friedrich, Metzelder, Mertesacker, Lahm, Borowski (Schweinsteiger 72), Ballack, Kehl, Schneider (Odonkor 83), Klose (Neuville 111), Podolski.
Subs Not Used: Jansen, Huth, Nowotny, Hanke, Kahn, Asamoah, Hitzlsperger, Hildebrand.
Booked: Borowski, Metzelder.
Italy: Buffon, Zambrotta, Cannavaro, Materazzi, Grosso, Camoranesi (Iaquinta 90), Perrotta (Del Piero 104), Gattuso, Pirlo, Totti, Toni (Gilardino 74).
Subs Not Used: Zaccardo, Barzagli, Peruzzi, Nesta, Amelia, Barone, Inzaghi, Oddo.
Booked: Camoranesi.
Goals: Grosso 119, Del Piero 120.
Att: 65,000
Ref: Benito Archundia Tellez (Mexico).
Fifa man of the match: Andrea Pirlo
TRIVIA
By defeating hosts Germany, Italy have reached their sixth World Cup final, denying Germany a record eighth final appearance. The Italians are now in position to become the second nation to have won at least four World Cup trophies.
Italy have now kept five clean sheets and have conceded only one goal (an own goal by Cristian Zaccardo) in the tournament. Their five shut-outs equals a record for a nation in a World Cup campaign.
Germany joined Chile (1962), Italy (1990) and South Korea (2002) as hosts to have been halted in the semi-finals. Their defeat was the third in a World Cup match that was decided in extra time. They also fell to England in the 1966 final (4-2) and to Italy in the 1970 semi-finals (4-3).
Trivia stats source: Infostrada Sports
We wtorek w pierwszym półfinale MŚ gospodarz turnieju Niemcy przegrały z Włochami 0-2. Bramki padły w ostatnich minutach drugiej części dogrywki.

Na początku spotkania Francesco Totti zdecydował się na bezpośredni strzał z rzutu wolnego. Uderzenie z 25 metrów zostało obronione z pewnymi problemami przez niemieckiego bramkarza. W 8. minucie po podaniu Lukasa Podolskiego Michael Ballack strzałem z ostrego kąta posłał piłkę wysoko ponad bramkę Włochów.

W 34. minucie Niemcy przeprowadzili kontrataku, który zakończył się strzałem Bernda Schneidera nad poprzeczką.

W drugiej połowie meczu poprawnie bronili bramkarze obydwu drużyn. W 61. minucie Gianluigi Buffon obronił strzał Lukasa Podolskiego, zaś Jürgen Klinsmann w przypływie bezradności rzucił bidonem z wodą.

Pięć minut przed końcem drugiej połowy Francesco Totti podawał do Simona Perrotty znajdującego się w polu karnym niemieckiego zespołu. Z bramki wyszedł Jens Lehmann i po wypiąstkowaniu lecącej piłki przewrócił Perottę. Sędzia nie przerwał gry.

Na początku dogrywki Alberto Gilardino strzałem po ziemi trafił w słupek. Minutę później Gianluca Zambrotta sprzed pola karnego uderzył w poprzeczkę.

W 118. minucie Jens Lehmann obronił strzał z dystansu Andrea Pirlo. Następnie w zamieszaniu po rzucie rożnym piłkę zdobył Pirlo i podał do boku do Fabio Grosso, który umieścił piłkę w siatce.

Po stracie bramki Niemcy próbowali wyrównać, jednak to nie oni zmienili wynik. W doliczonym czasie gry Alberto Gilardino, po ominięciu zwodem niemieckiego obrońcy, podał na wolne pole do Alessandro Del Piero. Ten strzałem pod poprzeczkę przypieczętował zwycięstwo swojego zespołu.

W trakcie całego spotkania Włosi oddali 15 strzałów na bramkę (w tym 10 celnych), a Niemcy 13 (dwa celne). Obydwie drużyny popełniły 40 fauli.

Niemcy zagrają w sobotę mecz o trzecie miejsce. Dzień później odbędzie się finał MŚ, w którym wystąpią Włosi. Wynik drugiego półfinału zadecyduje, z kim zagra Portugalia i Francja.