The American quickly took charge in the first set, breaking the 66th-ranked Goffin in the second and sixth games.
Underdog Goffin - who knocked out second seed Alexander Zverev in the last round - looked stronger in the second set, but ultimately couldn't replicate his feat with another top-10 scalp.
"I'm really happy with how I played… He's such an incredible returner, I had to stay extremely focussed, even more focussed than normal on my service games," said Fritz.
It is the first time US Open finalist Fritz has progressed past the third round in Shanghai.
He will next play either Novak Djokovic or Czech teenager Jakub Mensik, who will battle it out for the final spot in the semi-finals later on Friday.
World number one Jannik Sinner booked his place on Thursday, as did Mensik's compatriot Tomas Machac, who upset four-time Grand Slam champion Carlos Alcaraz.