The Bruins are the top overall seed and will host Ole Miss, Maryland & Bakersfield this weekend.
Bruins edge South Carolina and UNLV for final spot.
UCLA is one shot behind Alabama for 15th place and a spot in the fourth round.
The Bruins will be hosting an NCAA Regional for the fifth time in the last six seasons.
UCLA returns to the WCWS for the first time since 2010 following a Super Regional sweep of Missouri.
Kevin Kramer hit his 5th homerun, but UCLA dropped its first series of the season.
Brett Stephens homered and drove in a season-high tying three runs in tonight's loss.
The Bruins scored six unanswered runs to put them one win away from Oklahoma City.
UCLA's last two remaining singles players suffered losses on Saturday at Baylor's Hurd Tennis Center
Six teams are within seven shots of the cutline entering the third round.
Luke Persico drove in a team-high two runs and Kevin Kramer drew the game-winning RBI-walk.
Bruins 24th after first round.