Plutko stifled the Bulldogs on four hits and two walks in notching the victory in Omaha, Neb. He recorded two strikeouts.
James Kaprielian supplied a scoreless eighth inning and David Berg survived a scare in the ninth, recording the save after yielding a hit and a walk as the Bruins advanced to the winner's bracket.
UCLA trailed 1-0 after LSU's Mason Kratz socked a solo homer in the fourth but scored unearned runs in each of the sixth and eighth innings to grab the lead.
Eric Filia's sacrifice fly in the sixth sent Brian Carroll home after an error by catcher Ty Ross and Christoph Bono came home with the go-ahead run in eighth following a miscue by LSU shortstop Alex Bregman.
Bulldogs starter Aaron Nola was saddled with the loss despite not allowing an earned run on five hits over eight innings.
With the victory, UCLA moves on to play North Carolina state in Tuesday's winners bracket. LSU will play an elimination game against North Carolina.