Baker went 4-of-6 from 3-point range and Early connected on 4-of-7 long shots for the Shockers (28-8).
Fred Van Vleet added 13 points and Carl Hall contributed 10 for Wichita State, which became the first Missouri Valley Conference team to reach the Sweet 16 since Northern Iowa in 2010.
The Shockers will next play the winner of Sunday's game between 12th-seeded Mississippi and No. 13 La Salle in the West Regional semifinal.
Kelly Olynyk finished with 26 points for Gonzaga (32-3), which ended the season as the nation's top-ranked team and came into the contest with a 15-game winning streak.
Exploding whale video goes viral on Internet
Man spent 15 hours in jail for plugging electric car into an outlet at a school