Beltran finished with five RBI and Peter Kozma went 3-for-3 with a bases-clearing triple for the Cardinals, who reduced their magic number for clinching a National League wild-card spot to two.
They led the Los Angeles Dodgers by two games with four to play coming into Sunday's contest.
Lance Lynn (18-7) got the victory -- his fifth straight -- despite allowing four runs on six hits in a 5 1/3-inning outing.
Nationals starter Ross Detwiler (10-8) was rocked for seven runs (three earned) on four hits and five walks in just 2 1/3 frames.
Washington's magic number to clinch their first NL East title remained at one.