The first leg in Turin ended 2-2 and the return encounter finished in the same scoreline.
Inter had to play for almost an hour with ten men after Ivan Cordoba was dismissed and they did well to battle through for a draw.
However, they could not pinch victory as Juve held their nerve the better in the shoot-out to secure victory.
The lead changed hands twice in normal time, with Igor Tudor bringing Juve level shortly before the break after Adriano had given Inter an early lead.
Juve thought they had won the game when Alessandro Del Piero netted 12 minutes from time, but Daniele Adani popped up in injury time to take the game into an extra 30 minutes.
No goals were forthcoming, which forced the nerve-jangling penalty shoot-out.
Fabrizio Miccoli ended up being the hero of the night as he netted the vital penalty that gave Juve a 5-4 shoot-out win.
The villain of the piece proved to be Christian Vieri, as Inter's talismanic striker was the only player to miss in the shoot-out.
Juve will face Lazio in the final after the Roman club thrashed Milan in the other semi-final.
