The Turin side, who are on the verge of winning a sixth successive Serie A championship before facing Real Madrid in the Champions League final in Cardiff on June 3, won the domestic cup for a record 12th time.
"Compliments to the lads for what they did in the first half and for coming through a defensive test in the second," coach Massimiliano Allegri told reporters.
Allegri quickly turned his thoughts to the weekend when Juventus can clinch Serie A with a win over Crotone having missed their chance in a 3-1 defeat on Sunday away to AS Roma, who are four points behind with two fixtures remaining.
"We've won the first title, now we want to clinch the second, Sunday against Crotone, who have taken 17 points from the last seven matches," he said.
"It's going to be a difficult match. We'll have to play a mean game like this evening's."
Juventus, who beat Lazio in the final two years ago, settled the match in the opening 25 minutes with Alves putting them ahead in the 12th from a long, high cross by fellow Brazilian Alex Sandro.
The right back's volley was not as sweet as his goal in the Champions League semi-final second leg win over Monaco, but it proved just as effective, bouncing awkwardly on its way past goalkeeper Thomas Strakosha and inside the far post.
Lazio, who had hit the post in the sixth minute through striker Balde Keita, conceded a soft second goal 13 minutes later when Alex Sandro flicked on Paulo Dybala's corner and Bonucci nipped into the six-yard box to knock the ball in.
Lazio, who share the Olympic Stadium with AS Roma as a home ground in Serie A, made a better start to the second half and substitute Felipe Anderson's low shot brought a good save from Gianluigi Buffon's understudy Neto.
Neto then clawed a Ciro Immobile header off the line after Gonzalo Higuain had been involved in two chances for Juventus that went begging.
(Reporting by Rex Gowar; Editing by Toby Davis)
