The Brazilian was in trouble early on, as Nadal quickly set up three break points in the opening game of the match. However, he managed to reel off five straight points to register an early hold.
That only delayed the inevitable, as the Spaniard held comfortably before breaking through at the second attempt. The double break was secured four games later as Nadal walked the set.
Dutra Silva threatened to break at 1-0 up in the second set, but skewed an easy backhand wide as Nadal went on to hold. Once he did, it was the second seed who re-exerted his dominance to break for a 2-1 lead.
After securing a two-set lead with ease, the 27-year-old wrapped up victory without losing another game.
He will play Ivan Dodig in the next round at Flushing Meadows.