The Bruins (48-17) are one win from their first national championship in baseball and the school's record 109th in a team sport.
"Not much to get excited about," Savage said. "It comes down to tomorrow."
Mississippi State must win Game 2 on Tuesday night to keep alive its hopes for its first NCAA title in any sport.
UCLA made it 3-0 in the fourth on Eric Filia's two-out, two-run single off Chad Girodo, who replaced starter Trevor Fitts (0-1) in the second. That was the last of the Bruins' six hits.
Plutko (10-3) walked in the Bulldogs' run in the fourth.
UCLA is 40-0 when leading after seven innings. There was drama all the way to the end.
The estimated 8,000 Mississippi State fans at TD Ameritrade Park started the "Maroon and White" chant in the bottom of the ninth after C.T. Bradford and pinch-hitter Sam Frost singled to put runners on first and second with one out against closer David Berg.
Nick Ammirati flied out, and pinch-hitter Jacob Robson ended the game with his comebacker to Berg, who sprinted toward first base before underhanding the ball to Pat Gallagher.
Berg, who was making his 50th appearance of the season, earned his NCAA-record 24th save for 12⁄3 innings of work.
"Records are meant to be broken, but titles are what matter," Berg said. "So if we all win a national championship, I'll enjoy that. But right now I don't think about it at all."
The loss spoiled a splendid performance by Girodo, who pitched the last 72⁄3 innings. He allowed three hits, walked two and struck out nine. Both runs against him were unearned.
UCLA's Plutko improved to 7-0 with an 0.94 ERA in eight NCAA postseason games.
College World Series Finals
Monday • UCLA 3,Mississippi State 1 Bruins lead series 1-0 Tuesday • Game 2,6 p.m., ESPN Wednesday • Game 3,6 p.m., ESPN, if necessary