In capturing his sixth straight win, Fister (7-3) pitched 7 1/3 innings, giving up five hits and two runs with a walk and six strikeouts. Three relievers garnered the last five outs, with newly-minted closer Will Harris working the ninth for his fourth save as Houston (31-35) improved to 3-5 on its nine-game road trip that finishes Wednesday night.
Jaime Garcia (4-6) was tagged with the loss after going 6 1/3 innings, allowing eight hits and four runs, three earned. He walked none while fanning two.
St. Louis (35-31), which had won five consecutive games, closed within 3-2 in the sixth when Brandon Moss ended Fister's string of retiring 14 straight hitters with a two-out solo homer, his 15th of the year.
But Fister answered that with a two-out single off reliever Seung Hwan Oh an inning later, scoring Colby Rasmus and Carlos Gomez. Both runs were unearned, thanks to an error on first baseman Matt Adams on Gomez's bouncer.
It was the third and fourth RBI of Fister's big league career. Prior to that hit, American League pitchers had knocked in one run all season.
St. Louis initiated scoring in the bottom of the second as Matt Adams launched his ninth homer of the year, a 418-foot blast that barely cleared the glove of the leaping Carlos Gomez in center field.
Houston tied the score an inning later with George Springer's infield out that sent Gomez home. Gomez and Marwin Gonzalez started the rally with singles, then moved into scoring position on a sacrifice bunt from pitcher Doug Fister.
Colby Rasmus, playing his first game in Busch Stadium since the Cardinals dealt him in 2011 to help kick-start their World Series run, untied it in the fifth with a leadoff homer, his ninth home run of the season. Gonzalez added an RBI double that plated Gomez, who bunted for a hit and stole second, for a 3-1 Astros lead.
NOTES: Houston selected INF Danny Worth from Triple-A Fresno and started him at third base, batting him second. The 30-year-old Worth was hitting .340 with eight homers and 36 RBIs. ... St. Louis C Brayan Pena (left knee) halted his rehab assignment at Double-A Springfield to deal with a personal matter. He is 3-for-19 in six games dating to June 7. ... Astros RHP Luke Gregerson was placed on the family medical emergency list and the team also designated minor league RHP Juan Minaya for assignment.