The Rossoneri took the lead in the 24th minute as Alessio Romagnoli played a beautiful ball that put Rafael Leão through on goal. The Portuguese winger sent his shot past Pepe Reina to open the scoring.
Shortly before the break, Rafael Leão dribbled his way past his marker in the box to find Oliver Giroud, who tapped in his ninth goal of the season.
Just minutes later, Brahim Díaz led Milan on a quick counter and sent the ball out wide for Theo Hernández.
The full-back sent in a low cross to the far post that was sent past Reina by Giroud, who has scored a brace in consecutive games.
Lazio were quick to make substitutions after the half, but the additions of Luis Alberto, Pedro, and Lucas Leiva did not help the visitors take control of the match.
The Biancocelesti lost all hope of making an unprecedented comeback as Frank Kessie sealed the victory with 10 minutes left after capitalising on Lazio’s inability to clear the ball off a Daniel Maldini free-kick.
Milan advance to the semi-final of the Coppa Italia for the first time in two years, and they will face their cross-city rivals Inter Milan in the first match of the two-legged affair on March 2.