St. Louis starter Mike Leake was scratched because he was still recovering from having shingles. The Cardinals fell to 1-8 in interleague games at Busch Stadium this season.
Oakland trailed 2-1 in the eighth when Davis singled with one out against Matt Bowman (2-5) and Ryon Healy doubled, extending the longest active hitting streak in the majors to 13 games.
Seung Hwan Oh relieved and Max Muncy hit a grounder that Brandon Moss stopped with a dive, but Davis easily beat the throw to score the tying run. Brett Eibner followed with a sacrifice fly.
A's starter Zach Neal pitched a career-best six innings. Oakland pitchers held the Cardinals without a hit after the fourth inning, retiring the last 17 batters.
Daniel Coulombe (2-1) and Liam Hendriks combined for two perfect innings to set up Ryan Madson, who pitched a perfect ninth for his 26th save.