First-half goals from Dani Alves and Leonardo Bonucci were enough for the Bianconeri to claim the unprecedented record in Italy's premier cup competition, the 12th Coppa in the Turin-based club's history.
The former Barcelona full-back gave Massimiliano Allegri's side the lead after just 12 minutes as he volleyed home from a fine Alex Sandro cross, firing the effort into the turf and beyond Thomas Strakosha.
Juve pushed for a quickfire second and the Lazio stopper kept his side in the game with three great saves, denying Paulo Dybala twice from distance before making a brilliant block to stop Gonzalo Higuain slotting in from close range.
However, the Old Lady made the most of some slack defending to double their lead in the 24th minute, as Sandro flicked on a corner to allow the unmarked Bonucci to surge into the box and tap home.
Juve were tested in the second half as Lazio set about trying to claw their way back into the game and Simone Inzaghi's side pushed especially hard in the closing stages, but ultimately had little to show for their efforts.
The result means that Allegri celebrates his sixth trophy in only his third season in charge and sees the club one third of the way towards a possible treble of Serie A, Coppa Italia and Champions League.