The Chelsea striker had been dropped from the side's starting lineup after failing to score in their group games, but found the back of the net after coming off the bench in extra time.
The forward told FIFA.com: "I almost cried after my goal. It was the greatest moment of my life. Scoring at the World Cup at the age of 21 is something I've trained for since I was a boy."
Belgium will face Argentina in their quarter-final on Saturday.