Mouzakitis opened the scoring for Olympiacos from the spot, before second-half goals from Papakanellos and Bakulas ensured a dominant display was rewarded with silverware.
Indeed, Olympiacos could have taken the lead inside three minutes when Pneumonidis broke through on goal, only to be denied by Raveli.
Milan keeper Raveli also kept out a Papakanellos effort with a smart save, although Olympiacos were eventually rewarded for their persistence when Mouzakitis fired home from the penalty spot in the 60th minute.
There was no time for Milan to respond, as Papakanellos doubled the lead just moments later, before Bakulas sealed the triumph with a stunning scissor-kick.
Angelo Sina also impressed in the Olympiacos goal, producing a stunning save to deny Milan any chance of a consolation.
Olympiacos captain Thanos Koutsogoulas lifted the trophy aloft at the full-time whistle, sparking jubilant scenes among the players and fans.
Referee: John Brooks (England)
Yellow cards: K. Kostoulas, Papakanellos, Bakulas, Sina – Bartesaghi
OLYMPIACOS (Sotiris Sylaidopoulos): Sina, K. Kostoulas, Koutsidis, Prekates, Koutsogoulas, Alafakis (72’ Dama), Mouzakitis, Bakulas (88’ Tanoulis), Papakanellos (75’ Liatsikouras), Pneumonidis (88’ Gatopoulos), B. Kostoulas
MILAN (Ignazio Abate): Raveir, Manny, Simic, Ensiala (69’ Liberali), Bartesaghi, Stalmach (62’ Schimelhack), Malaspina, Geroli, Scotti, Sia (78’ Sala), Camarda (79’ Bonomi).
