The Netherlands and New Zealand battled to a 2-2 tie through regulation time and a 15-minute overtime. New Zealand could then put only one shot past Sombroek and the Netherlands advanced with a 3-1 decision in the shootout.
World champion Argentina won the other women's semifinal with a 2-1 edging of Britain.
Noel Barrioneuvo and Carla Rebecchi scored first-half goals for the Argentines, who reached the field hockey gold medal game for the second time. They won the silver medal at the 2000 Games in Sydney and settled for bronze in both 2004 and 2008.
The women from the Netherlands are looking for their second straight Olympic crown. The championship game will be played Friday.