Filippo Inzaghi began his Milan tenure with a 2-0 success over Renate last Wednesday and the Serie A giants always looked in control of proceedings at Stadio Comunale Brianteo.
Giampaolo Pazzini thought he had opened the scoring for Milan just after the half-hour mark, but the offside flag denied the Italy international.
Teenager Bryan Cristante was next to go close as Monza goalkeeper Sergio Viotti kept out his fierce low drive.
Inzaghi made a number of changes in the second half, but it was Niang - named in the starting XI - who was on hand to break the deadlock with a penalty after 69 minutes.
And Mastalli, who came off the bench to replace Andrea Poli, added the second six minutes later after collecting a pass by 16-year-old wonderkid Hachim Mastour.
Milan's pre-season preparations now continue in the United States, where they have friendlies against Olympiakos, Manchester City and Liverpool in the International Champions Cup.
