Napoli, the reigning Serie A champions, went ahead just before half-time when David Neres reacted quickest after Hojlund's low cut-back was only parried into his path by the Milan goalkeeper. Neres bundled the ball over the line to give Antonio Conte's side a deserved lead after a strong first-half showing.
Hojlund, formerly of Manchester United, then capped his performance on 63 minutes. The Danish forward collected the ball inside the area and drove a low, powerful shot beyond the keeper to double Napoli's advantage and put the result beyond doubt.
The win sent Napoli through to Monday's final, where they will face the winners of Friday's second semi-final between Bologna and Inter Milan.
Napoli captain Giovanni di Lorenzo praised the team's approach and intensity after the match. "We put in a big performance, both in commitment and intent. It's an important win for the team," di Lorenzo said.
Napoli are chasing their third Italian Super Cup title and their first since 2014. The victory also provided a timely lift for Conte's side after a league setback against Udinese last weekend.
In Serie A, Napoli are third in the table, sitting two points behind leaders Inter Milan and one point adrift of AC Milan, underlining how tight the title race has been this season.
The Italian Super Cup continues to feature the winners and runners-up from the previous Serie A and Coppa Italia campaigns and is scheduled to be staged in Saudi Arabia until 2029, with Riyadh once again providing the backdrop for the decisive matches.