By Rory Carroll
The Swiss third seed fired 35 winners and 10 aces to see off the outclassed Belgian in a speedy 80 minutes on a sunny day at Arthur Ashe Stadium.
The 38-year-old Federer was at his best when it mattered most, converting nine of his 10 break point opportunities to set up a meeting with Grigor Dimitrov or Alex de Minaur, who were playing their round of 16 match on the Grandstand court.
The only drama came early when Goffin, seeded 15th, broke Federer to take a 2-1 lead in the first set but the Swiss broke back in the next game and cruised to the finish line.
"I'm very happy with the level of play and the atmosphere," Federer said in an on-court interview.
(Reporting by Rory Carroll, editing by Ed Osmond)