Three-time European champion Inter, which 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 its first match. The second leg is Wednesday in Paris.
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.
However, 37-year-old Francesco Acerbi stunned the visitors by scoring in stoppage time — his first-ever goal in European competition — forcing extra time.
Frattesi then delivered the final blow, skillfully controlling a pass from Mehdi Taremi and evading young defender Pau Cubarsí before slotting the ball into the net. Barcelona nearly equalized once more, but Inter goalkeeper Yann Sommer made a critical fingertip save to deny Lamine Yamal and preserve the win.