The Swiss second seed overcame a third-set hiccup to beat Australian Groth 6-4 6-4 6-4 in the second round.
Groth held a 4-2 lead in the third set, only for Federer to respond with four straight games to advance at Flushing Meadows.
Federer said his efforts earlier in the set were the key to coming away with a comfortable win.
"I had my opportunities early on in the third as well, so I was just hanging on," he said.
"Maybe the pressure got to him a little bit just because of my opportunities I created."
Groth said he simply failed to produce his best in the big stages of the third set, one he feels he "should have won".
"It was an enjoyable experience," he said.
"I'm pleased playing in front of a crowd as big as the amount of people here, so to play on a packed house on Friday night against the greatest of all time, yeah, it's an unbelievable experience.
"To be honest, I feel I should have won the third set. Game points at 4-2, game points at 4-4. I didn't execute when I needed to."