Roma completed a 5-3 aggregate win in the two-leg semi-final against a sorry, injury-plagued Inter who have also been knocked out of the Europa League and seen their chances of Champions League football next season extinguished in the last month.
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Inter, trailing 2-1 from the first leg played three months ago, began promisingly when Brazilian striker Jonathan put them ahead in the 21st minute after a neat exchange of passes but it unravelled after half-time.
Destro levelled 10 minutes after the break, cleverly lifting the ball over Samir Handanovic after Erik Lamela slipped the ball between three defenders.
He then put Roma ahead 14 minutes later when he rolled in Federico Balzaretti's pass to finish off a counter-attack after an Inter attack broke down.
Torosidis crowned Roma's win when he flicked the ball over the head of a defender and then lobbed his shot over Handanovic from the edge of the penalty area.
Ricardo Alvarez pulled one back for Inter when he cut inside his marker and scored from the edge of the area, but it was too late for sorry Inter who have lost four of their last five Serie A games.
Inter were missing Diego Milito, out for the rest of the season, Antonio Cassano, Rodrigo Palacio, Walter Gargano, Yuto Nagatomo and Dejan Stankovic through injury while Alvaro Pereira and Fredy Guarin were suspended.
Roma face Lazio in the final on May 26.
