Substitute Davide Frattesi was the extra-time hero for Inter, firing home in the 99th minute to leave the Barcelona players slumped to the ground and all his Nerazzurri teammates — including those on the bench — racing to celebrate with him.
Moments earlier, Frattesi had been encouraging the already loud San Siro crowd to make more noise and the atmosphere grew even more feverish after his strike.
Inter, which lost the final to Manchester City in 2023, will face either Paris Saint-Germain or Arsenal in Munich on May 31. PSG beat Arsenal 1-0 in London last week in their first match.
There was little sign of the drama to come at halftime, with Inter comfortably leading 2-0 after Lautaro Martínez scored and earned a penalty, which was converted by Hakan Çalhanoğlu.
But Barcelona had been in that position before, having gone 2-0 down early in the first leg last week before securing a thrilling 3-3 draw.
And Eric García scored nine minutes after the break before Dani Olmo headed in the equalizer six minutes later.
Raphina appeared to have secured the win for Barcelona when he put the Spanish side ahead two minutes before full time, tucking away the rebound after Yann Sommer had saved his initial shot.
However, 37-year-old Francesco Acerbi astonishingly leveled in stoppage time — with his first goal in European competition — to add another 30 minutes onto the tantalizing encounter.
Frattesi had proved crucial off the substitutes' bench before, both for Italy and Inter, and so he was again, controlling Mehdi Taremi's pass and dummying round Pau Cubarsí before curling past Wojciech Szczęsny.
Barcelona almost leveled again but Sommer made a fingertip save to push Lamine Yamal's shot past his post.
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