Baxendale (8-5) allowed just three hits, giving way to Moore with one out in the seventh. He struck out five and walked one.
Kent State starter David Starn (11-4) walked three of the first four batters he faced and left after Vinson's two-out double in the sixth.
Kent State is the first team from the Mid-American Conference to make it to the CWS since Eastern Michigan in 1976.
Arizona 4, Florida State 3 - Johnny Field's RBI double in the top of the 12th inning lifted the Wildcats over the Seminoles.
Joey Rickard had doubled into the left-center gap for Arizona's first hit off Florida State closer Robert Benincasa (4-2), who came on in the ninth.
Field followed with his two-base hit to right, driving in Rickard.
The Seminoles scored two unearned runs off Arizona starter Kurt Heyer to tie it 3-3 in the sixth but had only three batters reach base the rest of the way.
Wildcats freshman closer Mathew Troupe (5-1) worked the last 22/3 innings for the win, striking out Devon Travis to end the game with a runner on third.
Arizona (44-17) plays UCLA on Sunday night in a meeting of Pac-12 cochampions.
The Seminoles (48-16) meet Stony Brook in an elimination game Sunday.