Jovic struck twice in the first half of the contest at San Siro, while 19-year-old Chaka Traore was delighted to score his first Milan goal on his full debut early in the second half.

Paulo Azzi grabbed a consolation for Cagliari in the 87th minute but there was still time for substitute Rafael Leao to score a fourth for Milan, who have not won the competition for 20 years.

Milan boss Stefano Pioli retained only two players from the starting line-up for Saturday’s Serie A win over Sassuolo – Theo Hernandez and Tijjani Reijnders.

Cagliari are sitting in the relegation zone in Serie A but it was Claudio Ranieri’s side who created the first big chance inside four minutes, with Andrea Petagna’s close-range header from a corner drawing a fine reaction save from 40-year-old Antonio Mirante.

Four minutes later Jovic was through one on one with Boris Radunovic after a perfectly-timed pass from Yacine Adli but the keeper was equal to his shot.

Antoine Makoumbou was the next to threaten the Milan goal when Petagna pulled the ball back into the middle of the box but his tame effort was straight at the keeper.

The breakthrough for Milan came in the 29th minute, with Hernandez the creator, picking out Jovic on the right of the box with a fine ball from the left.

The striker managed to evade his marker with his first touch before tucking the ball under Radunovic.

Three minutes before half-time, the summer signing from Fiorentina made it two goals in a game for Milan for the first time.

Again the architect was Hernandez, who drove down the left, cut into the middle and slid in Jovic, whose shot from a tight angle squirmed under Radunovic and into the net.

Five minutes after half-time, the widest smile in Milan belonged to 19-year-old Traore as he bagged a first goal in red and black.

It was a scrappy goal, with Alex Jimenez’s ball in from the left half blocked, Samuel Chukwueze failing to connect with his attempted shot and then Traore turning and guiding the ball under Radunovic.

The keeper will feel he should have done better but that took nothing away from the joy of Traore, who was mobbed by his team-mates.

Pioli turned to his big guns with 20 minutes left, sending on Leao and Christian Pulisic.

The visitors found something to celebrate in the 87th minute, Azzi’s strike from 20 yards taking a deflection and beating Mirante, but Leao had the final say, curling the ball beyond Radunovic in stoppage time.