Nakashima fell at the semi-final stage last year but he stayed perfect this week when he beat third-seeded Briton Draper 4-3 (8-6) 1-4 4-2 4-3 (7-5) on Friday to reach the final, where he will face Czech player Jiří Lehečka.
It was a hard-fought battle and Draper managed to save one match point with an ace to take the fourth set to a tiebreak.
But Nakashima sealed the victory at the second time of asking when Draper sent a forehand wide.
The fourth-seeded Nakashima, who lost to fellow American and eventual runner-up Sebastian Korda last year, served 15 aces and saved five of the six break points he faced.
Nakashima has won all four of his matches at the year-ending tournament for 21-and-under players, including a straight-sets victory over Lehečka in the group stage.
Dominic Stricker also won his three group-stage matches in Milan but was eliminated by the fifth-seeded Lehečka.
Lehečka was dominant from the outset as he eased to a 4-1 4-3 (7-4) 2-4 4-1 victory in 82 minutes.
After dropping the third set, Lehečka broke Stricker in the opening game of the fourth and never looked back, sealing the match when Stricker hit a return wide.
This is the fifth edition of the event, which features shorter sets of first-to-four games and other experimental format changes.
New rules include no changeovers after the first game of each set and only one sit-down per set after three games; a 15-second serve clock after aces, double-faults and unreturned serves; and coaching during an opponent's medical timeout or toilet break.
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