Wichita State used an 11-0 run late in the first half and early in the second to take a nine-point lead and pulled away further in the late stages for the win.
The Shockers (27-8) advance to Saturday's third round and a game with West Region No. 1-seed Gonzaga, which just escaped No. 16 Southern 64-58 later Thursday.
Pittsburgh wraps up its Big East Conference affiliation with a 24-9 record. The Panthers switch to the ACC next season.
Steven Adams had a dunk that put Pittsburgh up 21-19 with 3:38 to go in the first half. But Wichita State's Cleanthony Early dropped in a layup and a minute later Chadrack Lufile made a short shot that put the Shockers ahead for good.
The Shockers added three more points, including an Armstead layup before halftime and opened the second half by scoring the first four points -- Early converting an assist from Armstead, and Armstead making two free throws -- and were up 30-21.
Early backed Armstead with 21 points while Pittsburgh got a team-high 13 points from Adams.