The Swiss third seed powered past the 15th-seeded Goffin 6-2, 6-1, 6-4 and will face Czech sixth seed Tomas Berdych in the last eight.
Federer stormed into his 12th quarter-final at the Australian Open to extend his record for most quarterfinals at the year-opening Slam.
Federer leads Berdych 15-6.
It also brings up Federer's 47th Grand Slam quarterfinal, which is the most last-eight appearances in the Open era, ahead of Jimmy Connors.
Federer got off to a flyer and broke Goffin in the fourth game to seize early control and claimed the opening set in 21 minutes with another break of the Belgian's service.
Goffin offered no threat and Federer again got an early break to lead the second set, with the Belgian incapable to stemming the flow of winners.
Federer again broke on his fourth break point to crack the second set wide open, and he served out for a two-love lead in 50 minutes.
The Swiss great continued to turn the screws, with two more service breaks in the final sets as he romped to a quick-fire victory.
Goffin, who had posters of Federer on his bedroom wall when he was younger, has yet to beat his Swiss idol in four meetings.
Goffin was bidding to become the first Belgian man to reach the quarterfinals at the Australian Open.