Next up for Federer is Juan Martin del Potro, who beat Dutchman Robin Haase 6-2 6-4 in a night match at Crandon Park.
Federer has a 15-5 career record against del Potro, the 2009 U.S. Open champion.
"I would love to play against (del Potro)," Federer said, speaking before knowing who his next opponent would be. "We've had some epic matches against each other. I'm sure the crowd would love to see it."
Tiafoe provided a good competitive workout for the 35-year-old Swiss maestro in his first match since he won the BNP Paribas Open at Indian Wells on Sunday.
Tiafoe broke in the first game of the second set, but fourth seed Federer broke straight back with a sizzling backhand winner and another break was all he needed to clinch his 1094th career victory at tour level.
Tiafoe, ranked 101st in the world, has only four career victories, but he showed enough to suggest he will add to that number sooner rather than later.
Federer could be on course for a semi-final showdown with compatriot Stan Wawrinka, less than two weeks after they met in the Indian Wells final.
Top seed Wawrinka defeated Argentina's Horacio Zeballos in 65 minutes, firing seven aces in a 6-3 6-4 victory in less than favourable morning conditions.
"I'm really happy with the match today," Wawrinka told reporters. "It's quite tough conditions, raining and really windy today. It's really windy on the court, so it's never easy.
"I'm happy with the way I was moving, the way I was playing and my attitude in general was really positive," he added. "So it's a great match."
Austrian number six Dominic Thiem was the only high seed to suffer a loss on Saturday.
Thiem fell to 20-year-old Croatian Borna Coric, who overcame an embarrassing brain freeze in the final game to win 6-1 7-5.
Serving for the match, Coric stopped in the middle of a rally, challenging a line call, only to be reminded by the chair umpire that he had no challenges left.
Volatile Australian Nick Kyrgios won his match, and also received a code violation warning from the chair umpire for swearing at a spectator who called out during a point.
Kyrgios, the 12th seed, dropped his first two service games, but roared back to beat Damir Dzumhur 6-4 6-3.
(Reporting by Andrew Both in Cary, North Carolina and Gene Cherry in Salvo, North Carolina; Editing by Clare Fallon/Sudipto Ganguly)
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