A double from Egyptian Mohamed Salah on 66 and 90 minutes added to Stephan El Shaarawy's goal two minutes before the break to give Roma victory on the night.
Roma run away 3-0 winners, Inter run riot
But Lazio scored in either half through Serbian midfielder Sergej Milinkovic-Savic (37) and Italian forward Ciro Immobile (56) to book a third final in five years after beating Roma in 2013 for the title and losing to Juventus two years ago.
Simone Inzaghi's Lazio are fourth in Serie A and still in the running for Champions League football next season despite a chaotic start to the season when Marcelo Bielsa spent just two days in charge.
In-form Dzeko on target as Roma beat spirited Sassuolo
The six-time winners will meet either Napoli or Juventus in the final with the Turin giants leading 3-1 after the first leg.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ