In the end it took extra time, two astonishing Barcelona fightbacks and 13 goals - some of them mesmerising - to separate the two sides and see Inter prevail 7-6 on aggregate.
Substitute Davide Frattesi was the extra-time hero for Inter, firing home in the 99th minute on Tuesday (Wednesday AEST) 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, who lost the 2023 final to Manchester City, will face either Paris Saint-Germain or Arsenal in Munich on May 31.
PSG beat Arsenal 1-0 in London last week in the first leg of their semi-final.
There was little sign of the drama to come at halftime, with Inter comfortably leading 2-0 after Lautaro Martinez scored and earned a penalty, which was converted by Hakan Calhanoglu.
But Barcelona had been in that position before, trailing 0-2 early in the first leg last week before securing a thrilling 3-3 draw.
And Eric Garcia scored nine minutes after the break, before Dani Olmo headed in the equaliser 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 levelled in stoppage time - his first goal in European competition - to add another 30 minutes on to the tantalising 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 Cubarsi before curling past Wojciech Szczesny.
Barcelona almost levelled again, but Sommer made a fingertip save to push Lamine Yamal's shot past his post.
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