Juve went ahead when Dani Alves’s side-footed volley bounced into the corner.
Leonardo Bonucci sealed victory when he prodded in and Lazio, playing in their own stadium, could not find a way back.
Serie A leaders Juve can clinch their sixth successive Scudetto this weekend and meet Real Madrid in the Champions League final on 3 June in Cardiff.
Massimiliano Allegri’s side settled the match in the opening 25 minutes as they became the first side to win the competition three times in a row.
Lazio were competing in their third final in five years, hoping to inflict a measure of revenge after Juve beat them 2-1 after extra-time in 2015.
The capital club have not won another major honour since they beat neighbours Roma in 2013, with manager Simone Inzaghi prioritising the final by resting several key players for Saturday’s 3-2 defeat at Fiorentina.
The fourth-placed Serie A side, who are 15 points behind leaders Juve, made an energetic start and saw young striker Keita Balde Diao hit the post early on.
They created more chances after the break as Felipe Anderson and Ciro Immobile drew superb saves from Gianluigi Buffon’s understudy Neto, but by that time Juve had already done enough to seal victory.
Juventus manager Max Allegri:
“We have to compliment the lads for a great game, an extraordinary first half and Lazio deserve compliments for their entire campaign.
“Now we have another important game against Crotone to finish off the title.
“The first half had a very high tempo and we made the most of our chances, so we did well defending in the second half.
“It’ll be tough against Crotone, we need one victory and on Sunday it’ll be the decisive match of the season, so we need all our fans there. We have to play with the same determination we showed tonight.”
Lazio manager Simone Inzaghi:
“We are talking about the Champions League finalists, but tonight they were up against a Lazio side that had its say and was unlucky.
“In the first half, there was a handball to turn it on to the upright and that could’ve changed the game. A final is decided by incidents and tonight the incidents did not go our way.
“My lads were extraordinary this season and it was a very good performance this evening. It was an emotional night, we have to thank the fans and with a little bit more luck it could’ve gone differently. My players had a great season