Korda, who recorded straight-sets victories in his opening two games, cruised past home favourite Lorenzo Musseti 4-2 4-3 (7-4) 4-2 to reach the last four in Milan.
In Group B's other game, Baez became the first South American in the tournament's history to reach the semi-finals after defeating Hugo Gaston 4-3 (7-2) 4-2 4-2 in 65 minutes.
In a winner-takes-all Group A clash, fourth seed Nakashima rallied from a set down to edge past Holger Rune 3-4 (3-7) 4-1 4-1 4-3 (7-1).
Nakashima, who has now won 11 of his past 13 matches, will meet the undefeated Korda in the next stage.
Carlos Alcaraz had already secured his semi-final berth but maintained his unbeaten record in Thursday's other clash as he overcame Juan Manuel Cerundolo 4-0 4-1 2-4 4-3 (7-3).
With the victory over Argentine Cerundolo, Alcaraz becomes the youngest player to earn 30 tour-level wins in a season since Rafael Nadal, aged 18, did so in 2004.