Davis' basket and free throw with 16 seconds to play in overtime gave the Huskies (2-0) a 77-73 lead.
Talia Walton added 15 points and four blocked shots, and Mercedes Wetmore scored 12 for Washington.
Kacie Powell led Seattle (0-2) with 22 points and 14 rebounds. Ashley Ward scored 17 for the Redhawks and Sylvia Shepherd added 14 points.
Seattle outrebounded the Huskies 59-36, with Shepherd and Brenda Adhiambo each getting 10 boards for the Redhawks.