Furcal's solo home run in the fourth made the score 4-0 Cardinals and Adams, playing in his ninth major league game, added an RBI single.
Adams drove in two more runs with a sixth-inning double to break the game open while Daniel Descalso chipped in with a two-run home run for St. Louis, which had 14 hits in taking the opener of a three-game series in Atlanta.
Lance Lynn (8-1) struck out eight over seven solid innings for the victory, surrendering a pair of runs on five hits and one walk.
Braves starter Tommy Hanson (5-4) was tagged for six runs on eight hits, lasting only 3 1/3 innings.
Juan Francisco drove in a pair of runs for Atlanta, which dropped its eighth straight.