Goulbourne responded to the challenge of English hope Jade Johnson, who was the early leader of the competition with her first-round jump of 6.55m.
That mark was surpassed by Goulbourne in the fourth round and, although Johnson bounced back with a leap of 6.58m, the home favourite had to be content with silver.
The new Commonwealth champion said: "It was a great opportunity for me to be here.
"It feels pretty good although it's way below my best. I'm still grateful for it, I'm very happy."
Indian athlete Anju Bobby George took bronze with 6.49m, securing her country's first ever Commonwealth Games track and field medal.