Giacomo Bonaventura scored the game's only goal in the 13th minute as the Rossoneri stretched their unbeaten run to 10 matches in all competitions.
Milan did not let the setback affect them and went on to take the lead just before the quarter-hour mark, Bonaventura volleying Calabria's right-wing cross into the back of the net from close range.
The hosts continued to increase the pressure on their opponents and had the ball in the back of the net again on the stroke of half time, but scorer Leonardo Bonucci was deemed offside and the goal was ruled out.
Despite improving somewhat in the second 45 minutes, Sampdoria never looked settled as Milan continued to launch attacks into the opposition half.
However, Fabio Quagliarella came close to an equaliser late on, but he failed to test Gianluigi Donnarumma after peeling away from his marker, with the final whistle eventually blowing on a home victory.
AC MILAN (4-3-3): Donnarumma; Calabria, Bonucci, Romagnoli, Rodríguez; Montolivo (Locatelli 86'), Biglia, Bonaventura; Suso, Cutrone (Da Silva 73'), Calhanoglu
SAMPDORIA (4-3-1-2): Viviano; Bereszynski, Silvestre, Ferrari, Murru; Barreto (Verre 54'), Torreira, Linetty; Ramirez (Kownacki 72'); Quagliarella, Zapata (Caprari 53')