Ben Fielding and Brooke Ligertwood from the group, formed out of Sydney's Hillsong megachurch, received their award in the best contemporary Christian music performance/song category for "What A Beautiful Name".
Accepting the award at the event at Madison Square Garden in New York on Sunday, Fielding thanked his parents, wife, children and God.
He added: "No matter how far or how close you feel to God, no matter how great the distance, his love is greater, his name is more powerful, more wonderful, more beautiful than any other.
"May this song glorify the name above every other name, in the name of Jesus."
Meanwhile, CeCe Winans' picked up two Grammys for best gospel performance/song for "Never Have to Be Alone" and best Gospel album for "Let Them Fall in Love".
Bruno Mars was the big winner - taking six titles, including record of the year for 24K Magic.
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