"This is an absolutely incredible honour," said Fraser, who accepted the award with Australian songwriter Ben Fielding on stage inside Madison Square Garden, New York.
Fielding said: "No matter how far or close you feel to God or no matter how great the distance his love is greater, his name is more powerful, more wonderful, more beautiful than any other."
Brooke Ligertwood recently told Billboard the song was written to "serve people and link with them in the presence of God".
"When you connect with people, you can feel their spirits being lifted," she said.
"It's really the beauty of singing something about the wonder and power of Jesus."
Fraser has performed for the church under her married name, Brooke Ligertwood, since her wedding to Scott Ligertwood in 2008. The pair have two children together.
Hillsong's website describes the couple as part of the "core leadership team" at Hillsong Los Angeles.
In New Zealand, she's known for a string of classy pop hits, like Deciphering Me and Something in the Water, and she has won several New Zealand Music Awards.
The song was competing against Casting Crowns' Oh My Soul, Natalie Grant's Clean and MercyMe's Even If.
She's not the only Kiwi who was up for an award today: Lorde competed in the Album of the Year category against Kendrick Lamar, Jay-Z, Bruno Mars and Childish Gambino later today. Bruno Mars won the category with 24K Magic.
Read more: Brooke Fraser's secret Grammy nomination is for Hillsong's What a Beautiful Name
