Though Texas coach Shaka Smart made headlines by taking Virginia Commonwealth to the Final Four in 2011, the Rams had been eliminated in the round of 64 each of the last two seasons before beating Oregon State 75-67 on Friday.
VCU coach Will Wade, 33. said he deferred to his veteran players down the stretch.
"These guys have been through it," Wade said. "And you've got to roll with them, and that's what we did today. They came through big for us, like I knew they would."