Second seed Federer clinched a 6-4, 6-4, 6-7 (5/7), 6-2 victory over world number 69 Groth who fired a 147mph ace in the third game.
Federer will next face Spanish 20th seed Roberto Bautista Agut for a place in the quarter-finals.
"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.
"Now we are looking ahead and there are only big matches."
Federer through to the last 16 of Wimbledon
Federer on his way to victory over Groth. Photo: Tim Ireland/AFP
4 July 2015
17:36 CEST+02:00
Seven-time champion Roger Federer defeated big-serving Australian Sam Groth to reach the Wimbledon last 16 on Saturday.
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