The Shockers reached the title game of the West Region and will face Ohio State on Saturday with a trip to the Final Four at stake.
Ohio State's win was a thrilling 73-70 decision over Arizona while Wichita State methodically brought La Salle's unexpectedly long stay in the NCAA Tournament to a close.
La Salle had to play one of the First Four games last week just to get into the main field of 64 teams and the Explorers survived that test against Boise State. They then knocked off Kansas State and Mississippi to reach the regional semifinals, but they ran out of steam against the No. 9 seed.
Wichita State jumped in front 17-3 over the first 7 minutes and La Salle came no closer than eight points the rest of the way.
Armstead scored 18 points and had six rebounds while Carl Hall added 16 points and eight boards for the Shockers (29-9).
Wichita State finished second behind Creighton in the Missouri Valley Conference race and also lost to Creighton in the league tournament finals. Creighton won its NCAA opener against Cincinnati before falling to Duke.
Jerrell Wright led La Salle (24-9) with 15 points. The Explorers were the last of the five teams in the tournament from the Atlantic 10 Conference still playing and that league finished its NCAA experience this year with a 7-5 record. All five teams won at least one game.