Tony Cruz drove in two runs for the Cardinals, who have won nine of the last 10 games between the teams. St. Louis took control with a three-run second inning fueled by third baseman Anthony Rendon's throwing error.
Lynn (4-0) gave up one run and five hits over 5 2-3 innings in becoming the NL's first four-game winner.
Trevor Rosenthal worked the ninth for his fifth save, but not without difficulty. Washington put runners on second and third with one out, and Kevin Frandsen drove in a run with a groundout before Rosenthal struck out Jayson Werth on three pitches.
Zimmermann (1-1) allowed four runs, only one of them earned, in seven innings.