The veteran forward is still out after injuring his knee in May and needing surgery.
But Milan took the early lead when Davide Calabria put in a low cross from the right and Díaz’s effort squirmed through the hands of Samp goalkeeper Emil Audero.
Maignan had replaced Gianluigi Donnarumma in the offseason after the Italy goalkeeper moved to Paris Saint-Germain and he impressed on his debut, particularly with key first-half saves from Mikkel Damsgaard and Omar Colley.
Manolo Gabbiadini also hit the crossbar for Samp.
Olivier Giroud also made his debut for Milan after the veteran forward joined from Chelsea.
João Pedro scored twice as Cagliari fought back from two goals down to draw 2-2 against Spezia.
Emmanuel Gyasi gave Spezia a seventh-minute lead and Simone Bastoni doubled the visitors’ advantage in the 58th.