The 39-year-old Federer is into the fourth round of Wimbledon for a record-extending 18th time.
Roger Federer defeat Cameron Norris 6-4, 6-4, 5-7, 6-4 on Centre Court.
Federe had a slight shimmy in the third set as he missed two break points at 5-5 and was then broken at love by Norrie.
Following trading breaks in the fourth set, The eight-time Wimbledon champion broke again for a 5-4 lead.
He will take on No. 23-seeded Lorenzo Sonego of Italy on Monday.
It’s the 69th time that Roger Federe has attained the fourth round of a Grand Slam tournament, also a record.
Kyrgios withdraw with injury at Wimbledon
Norrie was the last British man remaining in the tournament.