An Adam Marusic own goal on 14 minutes and a Lautaro Martínez finish on 35 put the Nerazzurri firmly in control before half-time. Lazio threatened through Tijjani Noslin and substitute Boulaye Dia in the second half, but goalkeeper Josep Martínez made the saves that kept the clean sheet and the trophy.
It is the first time Inter Milan have won the league and cup double since José Mourinho led them to the treble in 2010 and the first time any Italian club has done it since Juventus in the 2017-18 season. Inter claimed their 21st Serie A title three rounds ago and now their tenth Coppa Italia.
Chivu, who played in that 2010 squad, spoke after the final whistle with emotion that was clear.
"It was the dream of mine, of the club, of the fans and of the team. The ambitions of Inter, its history in recent years, tell us to keep the bar high and to be competitive on all fronts. Sometimes it works, sometimes it doesn't — but what counts are the ambition, the work and the right motivations to reach goals and dreams. This group has done that from the very first moment, from when they accepted that we represent something more important than ourselves. Winning two trophies is never a given, and it is the merit of a group of marvellous boys."
On his own journey to this moment, he traced a long road.
"I have been on pitches all my life and I try to understand the world. I spent many years coaching youth teams because you need a process — you are never ready for certain things. And it helped me. From the bottom I learned a thousand things that have served me this year. And meeting this group has been fantastic. They put their faces on the line, they have ambitions, they find motivation and they put at the service of the other the best version of themselves."
Asked to give the season a mark out of ten, Chivu pointed to history.
"The first ten in history was given to the gymnast Comaneci, and she was Romanian. I also give a ten to the team. Next year the ambitions will be even higher. Ten with distinction — to all of them."
Chivu replaced Simone Inzaghi at the start of the season after the latter's exit following a campaign that ended with Inter finishing one point below Serie A champions Napoli. The Romanian has now delivered back-to-back trophies in his debut year at San Siro, and captain Martínez gave his own verdict.
"What mark would I give Chivu? Ten out of ten."