Edmund, who will break into the top 20 after defeating 12-time grand slam champion Djokovic, beat world number 10 Goffin 6-3 6-3.
The 23-year-old will now face either Denis Shapovalov or Milos Raonic in the last eight.
Edmund’s success was never seriously in doubt, as he outplayed an opponent he forced on to the back foot throughout and forced several errors.
He broke Belgian Goffin’s serve in the opening game of the first set, and retained control after that, losing just four points in his first four service games and taking it in 32 minutes by breaking Goffin again.
Edmund saved two break points on his first service game in set two, digging deep as Goffin tried to force his way back into the contest, before closing things out by clinching victory with a third match point in one hour and 12 minutes.