The Biancocelesti knew that they would progress if they could keep their opponents off the scoresheet and such a notion was evident in their extremely defensive mentality.
The Old Lady were allowed to dictate the tempo of the game but Alvaro Gonzalez's second-half header appeared to have justified Vladimir Petkovic's tactical decisions. Arturo Vidal thought he had taken the game to extra time when he struck late on but Sergio Floccari had other ideas with a header moments later to crush the visitors.
Juve was on top from the off and felt it should have been awarded a penalty after just eight minutes as Mirko Vucinic beat Federico Marchetti to the ball in the area and a collision followed. However, the referee only awarded a corner suggesting he believed the keeper made some connection with the ball.
Lazio struggled to ease that early pressure as the Bianconeri controlled possession, penning the Rome outfit back inside its own half.
But for all its time on the ball Antonio Conte's men struggled to find a way through the compact Biancocelesti defense. It was not until the 25th minute that the Serie A champions got in behind as Emanuele Giaccherini switched the play to Mauricio Isla but the Chilean's cutback was too close to Marchetti.
Both side's were defending in large numbers and after Miroslav Klose had seen a penalty appeal turned down on the half-hour mark the game's first save finally came in first-half stoppage time.
After Vucinic had seen his individual effort batted away by Marchetti, Giovinco popped up one minute later but after a brilliant turn he sent a tame attempt straight at the goal.
Those misses proved costly as eight minutes after the restart Lazio, against the run of play, took the lead. Cristian Ledesma's superb cross was flighted to the back post where Gonzalez ghosted in behind Federico Peluso to head in the opener.
The match momentarily opened up but Petkovic's men soon regained their composure and reverted to their conservative approach.
Eager to step up his side's search for a goal, Conte introduced Andrea Pirlo with 20 minutes remaining and the breakthroguh came in second-minute of added time. Giuseppe Biava failed to deal with a cross into the area and the ball fell to Vidal, who smashed it past Marchetti, breaching the previously stoic defense.
However Lazio was unperturbed and immediately ventured back up the other end and won its first corner. Stefano Mauri swung the ball in and Floccari got on the end of it, glancing a header past the idle Marco Storari and into the far corner.
Claudio Marchisio missed a near-open goal at the death after Giovinco's shot was parried aside in what proved to be Juve's last chance.
With its first win in 10 meetings against the Turin outfit, Lazio booked a spot in the final where it will face either fierce rival Roma or Inter.
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