The Argentinian, seeking to improve on his quarter-final showing at last year's US Open when the 2013 event takes place later this month, won 7-6 6-3.
South Africa's Anderson lost the first set tie-break to love and could not find a way back in the contest thereafter, with del Potro closing out victory to set up a semi-final against Tommy Haas.
Number three seed Haas proved strongest in the tie-breaks in his match against Grigor Dimitrov, winning the first 7/5 and the second 7/3.
The other semi-final will see America's John Isner take on Russia's Dmitry Tursunov.
Eighth seed Isner came from behind to wrap up a 6-7 (5/7) 6-4 6-4 victory over Marcos Baghdatis, while Tursunov knocked out Marinko Matosevic 6-3 4-6 7-6 (7/4) in the other quarter-final.
In the women's event, defending champion Magdalena Rybarikova booked her place in the last four with victory over top seed Angelique Kerber.
The Slovakian won 7-6 (7/0) 3-6 6-3 to set up a semi-final against fourth seed Ekaterina Makarova, who had an easier passage into the last four. Makarova's opponent, Monica Niculescu, retired through injury after losing the first game.
Alize Cornet will take on Andrea Petkovic in the other semi. Cornet knocked out Sorana Cirstea 7-6 (7/5) 6-2, while Petkovic saw off Paula Ormaechea 4-6 6-1 6-3.