Games two and three of the series will take place Saturday starting at 12 p.m.
The victory lifted ACU's season and conference marks to 27-11 and 13-7, while the Zias dropped to 12-31 and 4-17.
Crain (13-4) retired the first nine batters she faced, and didn't allow a base runner until the fourth when Melanie Alderette hit a leadoff single. Then in the seventh, the Zias finally lit their half of the scoreboard when Josette Aguirre came home on Kuuleiokealoha VonSchriltz' fly ball to center field.
ACU put runners on base against starter Amy Smith (8-17) in every inning, but could only score on the long ball. Gilliland connected first with her two-run shot in the second, and then Brigance went deep with two outs in the fifth. Brigance's home run was her fourth of the year, and for Gilliland, it was her second.
Madison Buckley led all Wildcats with two hits, finishing her night 2 for 4.