Willstrop, 33, followed up his shock win over Nick Matthew by beating Paul Coll 7-11 11-6 11-6 11-8.
If he beats Karim Abdel Gawad, it will be his first major world series final appearance since 2013.
Massaro beat Omneya Abdel Kawy to set up a semi-final with Perry, who edged out number two seed Raneem El Welily.
Former world number one Massaro, 33, saw off the eighth seed 11-4 12-10 11-6 at Grand Central Station, while 26-year-old Perry won 11-7 12-10 10-12 5-11 11-5.
English trio James Willstrop, Laura Massaro and Sarah-Jane Perry have reached the semi-finals of the Tournament of Champions in New York.