The seventh-seeded Anderson upended No. 1 seed John Isner of the United States 7-5, 7-6 (7-4), to reach only his third career final.
The South African fired 16 aces while improving to 3-3 against Isner and advancing to only his third career final.
There he'll meet unseeded Australian qualifier Matosevic, who bested Dudi Sela of Israel 5-7, 6-4, 7-6 (9-7) in a marathon contest to decide Saturday's other semifinal.
Matosevic was appearing in his first-ever ATP-level semifinal.