Texas (24-10) trailed by a point in the latter stages when Ridley's putback layup made it 82-81. After empty possessions both ways, Arizona State (21-12) point guard Jahii Carson drove baseline and dropped off a pass to Jordan Bachynski, whose thunderous dunk put the Sun Devils in front with less than a minute remaining.
With 32 seconds to play, Jonathan Holmes rebounded a Javan Felix airball and converted a layup plus a foul for an 85-83 Texas lead. Holmes was whistled for a foul on the other end, and Jonathan Gilling knotted the score at 85-apiece, setting up Ridley's heroics.
On the final touch, Holmes hoisted a deep 3-pointer that missed long off the backboard. After a scramble for the loose ball, Ridley came up with it and released his lefty layup, just over Bachynski's outstretched arm as the buzzer sounded.
Ridley paced the seventh-seeded Longhorns with 17 points, 12 rebounds and four blocked shots. Texas will face No. 2 Michigan in the Midwest Region round of 32 on Saturday.