Cooney, a 24-year-old left-hander brought up from Triple-A Memphis before the game, was given a 3-0 lead but lasted 2 1-3 innings, allowing three runs and seven hits.
Carlos Villanueva (2-1) followed and retired all 10 batters he faced. The Cardinals bullpen retired 19 of 21 batters during 6 1-3 innings of one-hit relief.
With the score 3-3 in the third, Adams hit a two-run homer off David Buchanan (0-5), who became the first Philadelphia pitcher to lose his first five starts in a season since Kyle Abbott in 1992.