Despite considerable pre-match hype about Johnson, fresh from victory at the Nottingham grasscourt event, there was to be no Independence Day party for the burly American, as Federer showed more than enough to suggest he remains on track for a record eighth Wimbledon men's singles crown.
While Andy Murray-supporting Brits have been rubbing their hands with glee over Novak Djokovic's shock third-round defeat, the biggest beneficiary of the Serb's removal may yet prove to be third seed Federer, who on Monday drew level with Martina Navratilova on a record 306 grand slam singles match wins.
In the quarter-finals, Federer will play Croatian ninth seed Marin Cilic who advanced after his opponent, Japanese fifth seed Kei Nishikori, retired injured while trailing 6-1 5-1.
American Sam Querrey followed up his shock Wimbledon defeat of Novak Djokovic by beating French veteran Nicolas Mahut 6-4, 7-6 (7/5), 6-4 on Monday to reach his first Grand Slam quarter-final.
Querrey, the 28th seed, is the first American in the last-eight at Wimbledon since Mardy Fish in 2011.
He will face either Canada's Milos Raonic or David Goffin of Belgium for a place in the semi-finals.
On the women's side, lovakia's Dominika Cibulkova bundled third seed Agnieszka Radwanska out of the fourth round of Wimbledon on Monday, saving match point on the way, less than two weeks after beating her in the Eastbourne warm-up tournament.
In an energy-sapping contest between power and touch, Cibulkova used a thunderous serve and thumping forehand to wear down Radwanska 6-3 5-7 9-7.
Cibulkova broke the Pole, whose all-court game lacked energy and precision at the start, in the fourth game of a lacklustre first set and took the set with a big serve that Radwanska knocked tamely into the net.
The pair exchanged breaks throughout the second set and Radwanska saved a match point in the ninth game, finding some verve and precision to grab the set from the disappointed Slovak.
The two women ramped up the quality in the final set, hitting the lines, producing deft dropshots and fighting through exhausting groundstroke rallies to the delight of the gripped Court Three crowd.
It was the 13th contest between the pair, both 27, and by now they were shrieking with effort as they ran the lines.
Cibulkova, ranked 18 in the world, survived a monumental 11th game in the set, saving match point with a forehand winner.
It was another thumping forehand that brought her victory on the second match point of the final game for her sixth win against the Pole, a finalist here in 2012.
The Slovak will meet either Ekaterina Makarova or Elena Vesnina, both of Russia, in Tuesday's quarter-finals.