The Owls (42-16) and Wildcats (43-17-1) will meet again Monday night, with the winner advancing to the super regionals.
Wall (7-5) struck out four and walked one in the longest outing of his career. He's the first Rice pitcher to throw a shutout in the NCAA tournament since Justin Crowder in 2002 against LSU.
The Owls (42-16) finished with 11 hits, including two each by Anthony Rendon, Steven Sultzbaugh and Michael Fuda. Pinch-hitter Jess Buenger drilled a three-run homer over the right-field wall in the eighth.
Todd Vogel (4-2) gave up three runs on six hits in 4 1-3 innings in the loss.
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