Roger Federer of Switzerland wins against Daniel Evans of Great Britain during their Round Three Men's Singles match at the 2019 US Open at the USTA Billie Jean King National Tennis Center in New York on August 30, 2019.
The first four games went with serve, with Evans saving three break points in the last of these, but thereafter the 20-time grand slam champion dominated without having to reach top gear.
Evans was given a code violation for smashing his racquet at the end of the second set and though he broke Federer for the first time to reduce the score to 2-1 in the final set, this proved to be the final flourish of the last Brit in the men's tournament.
Federer says he expects "quality baseliner" Goffin to pose a sterner test.
"I expect it to be tough, not like today anyway," Federer said.
Elsewhere, Australian Alex de Minaur upset seventh-seed Kei Nishikori 6-2, 6-4, 2-6, 6-3.
The 2014 US Open finalist committed 60 unforced errors and seven double faults in crashing out of the tournament.
De Minaur will next play the winner of the match between Grigor Dimitrov and Kamil Majchrzak.