The Waves (42-16) got past the regional round for the first time since winning the College World Series title in 1992.
The Mustangs (47-12) had come all the way back from a 5-0 deficit to tie it at 6 with a two-run rally in the bottom of the eighth. Left-hander Taylor Chris took the loss after mostly handcuffing Pepperdine through a season-high 61/3 innings in relief of starter Danny Zandona.
Earlier, Zach Zehner homered and Cal Poly hung on for a 6-5 victory over Sacramento State to get another shot at Pepperdine.
Oklahoma State 6, Cal State Fullerton 4: Tim Arakawa lined a two-run single with the bases loaded in the seventh inning to drive in the tying and go-ahead runs as the Cowboys eliminated the Titans in Stillwater, Okla.
Top-seeded Oklahoma State (48-16) beat Fullerton (34-24) for the second straight day and advanced to the super regional next weekend. It will be Oklahoma State's first trip to a super regional since 2007 and just its second overall.
The Titans earlier in the day beat Nebraska, 4-3.
Irvine was limited to two hits. The teams play again Monday at 8 p.m.
Late Saturday night, Irvine beat Oregon State, 14-2, as Elliot Surrey allowed two runs and three hits and struck out eight.
Oregon State earned another shot at Irvine with a 6-1 win over Nevada Las Vegas earlier on Sunday.
The game will resume in the top of the seventh inning with Long Beach State leading, 5-4, with runners on first and second base and one out.
The winner of the completed game will face the College of Charleston on Monday, needing to beat the Cougars twice to advance.
Texas Christian 6, Sam Houston 1: Freshman Tyler Alexander threw a six-hitter and the Horned Frogs advanced to their fourth super regional in six years, beating the Bearcats for the second time in two days.
On Saturday, Boomer White's go-ahead RBI single in the 22nd inning led TCU to a 3-2 victory in the second-longest game in NCAA tournament history.
The game, which lasted 6 hours and 54 minutes, is surpassed only by Texas' 3-2 NCAA tourney victory over Boston College in 25 innings on May 30, 2009. It also tied for the third-longest overall contest in Division I history.