Jordan Walker and Tommy Edman also hit homers for the Cardinals, who won for the third time in a row and the fifth time in six games.
Lawrence Butler hit his first career homer, a two-run blast, as the A's lost their fifth straight game and their seventh in eight tries.
St. Louis outhit the A's 14-6 but went 2-for-13 with runners in scoring position while stranding 11 on base.
Cardinals starting pitcher Dakota Hudson (4-0) allowed two runs on five hits in 6 2/3 innings while winning his third straight start. He struck out three and walked one.
Spenser Watkins (0-1) suffered a difficult loss in his A's debut. He allowed five runs on seven hits and two walks in 4 1/3 innings.
The Cardinals took a 4-0 first-inning lead. Lars Nootbaar hit a single, Paul Goldschmidt followed with an RBI double and Arenado ripped his two-run homer.
Walker's home run capped the outburst.
Hudson walked Nick Allen and hit Esteury Ruiz to start the third inning. Allen advanced on a flyout and Ruiz stole second base, but Hudson struck out the next two batters.
The Cardinals increased their lead to 5-0 in the fourth inning when Walker walked and scored on Andrew Knizner's double. Knizner advanced on a flyout, but was doubled off third base after left fielder Tony Kemp made a terrific catch down the line.
Knizner hit a single in the sixth inning and took third on Tyler Motter's double. Nootbaar walked with two outs, but Goldschmidt struck out to leave the bases loaded.
The A's finally got to Hudson in the seventh inning. Tyler Soderstrom hit a one-out single and Butler followed with his homer.
St. Louis loaded the bases again in the seventh inning, but Motter hit an inning-ending grounder.
Edman hit his homer in the eighth inning to increase the St. Louis lead to 6-2.
—Field Level Media