Finch, the Pac-10 Player of the Week for last week's action including four homers and a no-hitter in UA's Arizona Wildcat Softball Classic tournament, faced the minimum 15 batters and struck out 10 against Drake in UA's second game of the day.
UA's Becky Lemke threw a three-hitter in Arizona's opening victory in the tournament, 3-0 against DePaul.
Arizona is 16-1 on the year and ranked No. 3 in the latest coaches poll. The Cats face host Alabama at noon (CST) and Georgia Tech Saturday, then depending on seeding enter elimination play in the tournament.
Finch's perfect game was her third career no-hitter and second in as many weeks.