Granollers moved into a 5-2 lead in the first set of the third-round tie before inclement weather forced a two-hour suspension in play.
The Spaniard went on to close out the opener, but 17-time grand slam winner Federer assumed complete control thereafter to record a 4-6 6-1 6-1 6-1 success.
When asked about his change of fortunes after the rain delay, the 33-year-old pinpointed a lack of wind as a key factor in his victory.
"Well, I definitely I guess played better after that [the rain]," he said.
"But then again, the first seven games all happened very quickly.
"I think the biggest difference was the wind. It was quite windy when we got out. When we came back, basically it was gone."
"It also felt quite different because the wind has that effect of air-conditioning a little bit for the players; whereas when it's not windy you really feel the humidity and the heat. So I think that was a big change."
Federer, playing in his 60th grand slam, appeared unaffected by the sticky conditions as he moved a step closer to a sixth US Open title.
"Yeah, it's been good for a while now, [my conditioning]. I think especially now it's been really excellent the last three matches here at the US Open," he said.
"I feel very explosive, quick. Like you say, the coordination is there, as well. I feel like I've gotten used to the hard courts by now. It's really working well. I'm very pleased."
Federer will now turn his attention to Roberto Bautista Agut after the Spanish 17th seed won through to the fourth round thanks to a straight-sets win over Adrian Mannarino.
"[I've] never played him. I think he's done extremely well," said Federer of his next opponent.
"He's quick on his feet. He doesn't miss much. He's consistent. He's got a pretty good first serve. He's overall a solid player.
"I would assume he's fit, too, because he comes from the Spanish tennis school, which they just know how to train hard. They never get tired. They're always ready to go."