Inter Milan battled for more than an hour with 10 men to eliminate Barcelona 3-2 on aggregate and advance to next month's Champions League final.
Having lost the first leg semi-final 1-3, defending champions Barcelona won the second leg 1-0 at the Nou Camp, but the result failed to see them advance.
Jose Mourinho side will play Bayern Munich in the May 22 final in Madrid, their first final of Europe's elite club competition since 1972.
Portuguese Mourinho, a former assistant trainer at Barca, ran on to the pitch to celebrate with his players at the final whistle and clashed with Barca goalkeeper Victor Valdes as a hail of objects rained down from the stands.
"It's an incredible joy, I've won the Champions League (with Porto in 2004) but I must say today was better than winning the Champions League," Mourinho told Rai TV.
After losing last week's semi-final first leg in Milan 3-1, Barca coach Pep Guardiola fielded an ultra-attacking formation and with the home fans roaring their support the visitors' defence came under immediate pressure.
For all their early possession Barca were struggling to create chances and a Pedro volley in the 22nd minute that flashed narrowly wide was their first real effort on goal.
Tempers boiled over five minutes later when Inter midfielder Thiago Motta flung out an arm in a challenge with Sergio Busquets which sent the Barca player tumbling to the turf.
Former Barca player Motta, who had already been booked, was sent off, sparking a melee in which he grabbed Busquets by the back of the neck before being shepherded away.
The dismissal was the cue for a magnificent rearguard action from Inter, who dealt with almost everything the fearsome Barca attack could throw at them.
Barca pressed and Lionel Messi curled a shot that Julio Cesar acrobatically tipped around the post before a thunderous Zlatan Ibrahimovic flashed just wide.
As the clock ticked down, Guardiola sent centre back Gerard Pique forward to play as an extra striker and it was his superbly taken goal in the 84th minute that gave Barca hope.
With the noise levels rising ever higher, they pressed for the goal that would send them through and had a goal at the death disallowed from Bojan Krkic when Yaya Toure was adjudged to have handled the ball in the build-up.