The Cardinals scored four first-inning runs off Robbie Ray on Tuesday, but had to wait a little longer Wednesday with Patrick Corbin limiting them to Mark Reynolds' homer in six innings.
St. Louis quickly took advantage after Corbin left, scoring twice off David Hernandez (1-4) in the seventh. Kolten Wong had an RBI double and Matt Carpenter a run-scoring single in the inning.
Lackey (11-8) bounced back from a shaky start, giving up a solo homer to Paul Goldschmidt in the first inning and little else. Trevor Rosenthal worked around a walk in the ninth for his 40th save.
St. Louis moved to 36 games over .500 (81-45), its highest since finishing the 2005 season plus-38. The Cardinals have won 12 of 13 against Arizona.
