Federer has feasted on Australian opponents in grand slams over the years, piling up an 18-1 record against men from Down Under, and Groth, who was facing a top 10 opponent for the first time, proved little more than a distraction to the Swiss maestro.
The burly Groth, who had a brief stint as an Australian Rules football player in 2011, stepped onto Arthur Ashe Stadium court looking ready for a fight but in the end could only wave the white flag as Federer closed out the match with an ace, sweeping through the final four games.
Throughout the one hour and 48 minutes contest the Australian took his best shots at the 33-year-old, including booming serves of over 140mph.
"The 142, honestly I hit it and I turned around," said Federer, who will next face Spain's Marcel Granollers, a 7-6(6) 6-7(3) 7-6(5) 3-6 6-4 winner over 25th seed Ivo Karlovic.
"I didn't know if it went into the stands or the bottom of the net or on the other side. I just felt like I hit it clean.
"The 147 one I felt like I was there and felt like I had more control on it.
"The difference between 142 and 147, there's none really in the racquet. I think once you pass the 135 range everything is just really fast."
MAN IN BLACK
Federer, dressed all in black, took a few games to feel out his opponent before making the breakthrough to go 4-3 ahead, then held serve to take the first set.
The second set opened with the two men trading breaks, with Federer again gaining the upper hand and breaking Groth a second time to go up 5-4 and serve out for a 2-0 lead.
The 26-year-old Australian said he tried to focus on his own game and not get swept away by the crowd's support for Federer.
"To be honest, for me, I was trying not to get caught up in the whole Roger act out there," he said. "You walk out, you get a few cheers. He walks out and the crowd goes ballistic.
"So from the word go you know he's there. I was honestly just trying to focus on what I was doing.
"He's got an aura because of how good his tennis is. Yes, there's an aura because of what he's done, but his tennis speaks for itself.
"You don't win 17 grand slams if your tennis is not that good. I knew I was playing Roger Federer."
Groth, who watched compatriot Marinko Matosevic lose in straight sets to Federer in his opening match, dug deep in the third set, scratching out a 4-2 lead.
However, five-time champion Federer answered back with a break of his own and then raced through the next three games to seal the victory.
(Editing by Peter Rutherford)
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