Novak Djokovic ended Gilles Simon's Paris Masters bid on Thursday, while Kei Nishikori was forced to withdraw from his match against Richard Gasquet.
Gasquet advanced to the quarter-finals after Nishikori retired while trailing 6-7 (3-7), 1-4.
The Japanese ace needed treatment during the match and appeared to be suffering from a neck injury.
Elsewhere, top seed Djokovic kept his hopes of a record sixth ATP World Tour Masters 1000 crown alive after beating Simon 6-3 7-5 in an hour and 38 minutes – even if it was hardly a vintage performance.
Djokovic surrendered an early break, but hit back strongly to take a 4-2 lead before closing out the first set.
The second set featured an incredible nine breaks of serve, with Djokovic eventually clinching the set after claiming a fifth break to Simon's four.
Scotland's Andy Murray was the first man to reach the quarter-finals on the day after dropping just one game in his 6-1 6-0 victory over the Belgian.
Murray had won all seven of their previous encounters, and needed just 53 minutes to make eight in a row.
"It was difficult for me to do something today," said Goffin, who will meet Murray again in the Davis Cup final later this month.
"I felt tired. My body was on the court, but there was nobody on the inside."