The Spanish holders won the semi-final second leg 1-0 but Inter went through 3-2 on aggregate after a pulsating encounter at Barca's Nou Camp stadium to reach their first final of Europe's elite club competition since 1972.
They will play Bayern Munich in the final at Real Madrid's Bernabeu stadium on May 22.
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Mourinho, a former assistant coach at Barca, raced onto the pitch at the final whistle, his wild eyes fixed on the small section of triumphant Inter fans as he pointed a celebratory finger to the sky.
He clashed with Barca goalkeeper Victor Valdes as a hail of objects rained down from the stands before he returned to the embrace of his ecstatic players.
"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.
MAGNIFICENT REARGUARD
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 clutching his face.
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 led 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.
Champions League top scorer Lionel Messi curled a shot that Julio Cesar acrobatically tipped around the post before a thunderous Zlatan Ibrahimovic free-kick flashed just wide.
As the clock ticked down in the second half, substitute Bojan Krkic missed a sitter of a header but a minute later centre back Gerard Pique, moved by coach Guardiola to a last-ditch striking role, made amends with a superbly taken goal in the 84th minute that gave Barca hope.
The Spain international controlled the ball in the penalty and showed a striker's touch to spin away from Cesar and the Inter defenders and slot into an empty net.
With the noise levels rising ever higher, Barca pressed for the goal that would send them through and had an effort from Krkic at the death disallowed when Yaya Toure w
