Edmund, who will break into the top 20 [when verified] 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.
“There were lots of good things. I managed my game very well today,” Edmund told Sky Sports.
“My game is one of those where the better I manage it and pick my moments to be aggressive, then I play well.
“I served really well today. It got me through easy games and also got me out of some tricky situations.
“He is a top player, top 10 in the world, so it is very pleasing.”
Meanwhile, former British number one Andy Murray is doing “everything he can” to be fit for Wimbledon, according to his mother Judy.
The two-time Wimbledon champion has been sidelined since last year’s tournament, and underwent hip surgery in January.
Murray’s mother Judy has insisted the 30-year-old can still be ready to hit form come Wimbledon’s July 2 start.
“His goal was always to be ready for the grass-court season and, fingers crossed, that will happen,” Judy Murray told the BBC.
“I’m sure when he’s got some news he will share that.”
Murray is unlikely to feature in a tournament in Loughborough later this month, while the Scot has publicly committed himself to Holland’s Rosmalen grass court tournament that starts on June 11.
“The strength and depth of men’s tennis is so great that I don’t think anybody would want to come back into that environment unless you are 100 per cent,” said Judy Murray.
Asked if she had any fears about his career being over, the former Fed Cup captain added: “I don’t think so; he’s still got a lot of things he wants to achieve in the game.”