The game was the Wildcats' first extra-inning game of the season and took nearly two hours and 30 minutes to play.
Finch held ASU to two hits and struck out 12 two improve her record to 15-0. Toni Mascarenas doubled to lead off the inning and Leneah Manuma was hit by a pitch to set up the only scoring of the game. Mascarenas had three of UA's six hits.
No. 2-ranked Arizona improved to 40-4 and 4-2 in the Pac-10. No.8 ASU dropped to 30-10 and 5-2.
UA's Finch and ASU's Erica Beach and Kirsten Voak held each team hitless until the sixth inning. The Sun Devils' Missy Hixon singled to right with two outs and Mascarenas singled to left in the bottom of the frame off Voak.
Beach started the game for Arizona State, Voak pitched in the first, Beach re-entered in the second and Voak re-entered the circle in the sixth. Voak (12-4) took the loss.
Lauren Bauer and Nicole Giordano reached on walks to lead off the Arizona first, but ASU pitched out of the jam by getting the middle of the lineup on infield pop outs.
Mackenzie Vandergeest was hit by a pitch and Allison Andrade drew a walk to put two UA runners on with one out in the fifth, but Beach got Jenny Gladding and Lauren Bauer to pop out to end the threat.
Karen Brun sent Wildcat leftfielder Giordano to the fence for a long out in the top of the seventh, but Finch caught a liner and struck out Beach to end the inning.
ASU loaded the bases but came up empty in the ninth. Finch walked Kara Brun with two out, Phelan Wright singled her to third and Finch intentionally walked Beach. She then struck out Kristin Swetel to end the inning.
UA squandered a bases-loaded situation in the bottom of the ninth when Toni Mascarenas, pinch-hitter Erika Hanson and Finch each had singles with one out. But Voak struck out Lindsey Collins and Vandergeest to thwart the rally.
The two teams play again Saturday night at 7 p.m.