Federer's Australian opponent holds the record for the fastest ever delivery in tennis and regularly launched 140mph missiles but only briefly threatened the Swiss's serene progress to the fourth round and eventually succumbed 6-4 6-4 6-7(5) 6-2.
Groth briefly slowed Federer's bid for a record eighth Wimbledon title by holding serve throughout the third set and forcing a tiebreak that he clinched when the second seed misjudged a forehand at set point.
Yet Federer was in no mood to let his stranglehold slip and broke for a 2-0 lead in the fourth and then again to close out the match.
The imposing figure of Groth rekindles memories of the dominant figures at Wimbledon in the 1990s when a sledgehammer serve could propel you into the latter stages at the All England Club.
Nowadays, however, the pinnacle of the men's game is populated with more refined talents and none more so than Federer, whose bid for an 18th grand slam title looks compelling on the evidence of Wimbledon's opening week.
He scythed through the first two sets against Groth breaking once in both and even out-aced the Australian 6-3 in the second.
Groth, whose fastest delivery of 147 mph fell just short of Taylor Dent's 2010 Wimbledon record of 148, held his nerve throughout the third, but his inability to lay a glove on the Federer serve proved his ultimate downfall in the match.
He could not engineer a single break point throughout the two hour 16 minute contest and was put to the sword when Federer fired a rasping return on match point that dipped into Groth's shoelaces as he charged to the net.
"I am very happy. It has been a hot week the first week but thankfully I have had easy matches going through without too many long four or five setters," said Federer, who now faces 20th-seeded Spaniard Roberto Bautista Agut.
"Now we are looking ahead and there are only big matches."
(Reporting by Toby Davis; Editing by Ken Ferris)
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