The first-round victory created a West Virginia-Duke matchup Saturday in the West Region.
The Mountaineers gave the Big East Conference a 4-0 record on the first day of the tourney with four more teams from that conference scheduled to play Friday.
Ruoff scored 21 points and Nichols had 14 for the seventh-seeded Mountaineers (25-10). Da'Sean Butler added 19 points for West Virginia.
Arizona was appearing in the tournament for the 24th consecutive season, the event's longest current streak. But the Wildcats had their season end at 19-15.
Chase Budinger scored 23 points for Arizona and Jordan Hill had 16.
The game also brought an end to Kevin O'Neill's tenure as interim coach of the Wildcats. O'Neill took over for Coach Lute Olson, who asked for a year's leave of absence for personal reasons but who plans to return for next season.
After one day of the tournament, only two lower seeded teams had advanced -- Texas A&M (seeded ninth in the West) and Kansas State (seeded 11th in the Midwest).