The Coppa Italia appears to represent Juve's best chance of silverware this season after a 15-point deduction ended their slim Serie A title hopes, and the hosts were good value for their win after dominating for long periods.
Massimiliano Allegri's men missed two good chances before hitting the front on the stroke of half-time, with Bremer flicking Filip Kostic's inch-perfect delivery home.
Juve was rarely troubled at the other end as Maurizio Sarri's visitor disappointed in the final third, and it will face its Derby d'Italia rival across two legs in the last four after this routine win.
Kostic drew a fingertip save from Luis Maximiano as Juve got on top after a tight opening to the contest, before Adrien Rabiot headed straight at the goalkeeper when left unmarked just before the half-hour mark.
The Bianconeri made their pressure count one minute before the break as Bremer met Kostic's inswinging cross with a glancing header, which beat Maximiano to nestle in the bottom-left corner.
Luis Alberto saw a long-range strike deflect narrowly over as Lazio improved following the half-time introduction of Pedro, while Danilo Cataldi worked Mattia Perin with a 25-yard free-kick.
Juve substitute Moise Kean forced Maximiano into action at his near post following a rapid break with 20 minutes remaining, as the hosts looked to put the game to bed.
Adam Marusic fizzed a long-range effort wide of the bottom-right corner as Lazio continued to hunt a leveller, but that was as close as it came to breaking down a resolute Juve backline.