St. Louis won three out of four in the series and has captured nine of its last 13.
The Cardinals had seven hits in the game and used three of them, along with a stretch of wildness by Christian Friedrich (4-6), to put together their big inning.
That brought up Beltran, whose double to center added to the lead. The final run of the inning scored on a fielder's choice grounder by Allen Craig.
Winning pitcher Lance Lynn (11-4) left the game after throwing six shutout innings and 104 pitches. He gave up four hits and struck out seven.
Tyler Colvin hit a two-run homer for the Rockies in the eighth.