Cuddyer's clout in the second inning put the Rockies ahead to stay. He later added run-scoring singles in the third and fourth innings, chasing home three more runs.
Nolan Arenado also socked a bases-empty homer while DJ LeMahieu and Wilin Rosario each added an RBI as Colorado earned a split in its four-game road series.
Jorge De La Rosa (8-4) broke a personal three-start winless streak, yielding two runs on seven hits in a six-inning performance.
He exited with a 7-2 lead but Rex Brothers was called on to notch his fourth save after Washington made it close with four runs in the eighth off Matt Belisle.
Nats starter Ross Detwiler (2-6) was torched for seven runs on nine hits over just 3 2/3 innings.
Jhonatan Solano delivered a late two-run, pinch-hit double for Washington, but it wasn't enough as the Nats came up a bit short.