Jennifer Nettles, half of the duo, told the audience the award is shared by the performers and writers of the song, as well as its producer Byron Gallimore, a man Nettles described as "part therapist, part magician."
"Thank everybody for believing in a song that's almost a 5-minute-long acoustic song," Nettles' partner Kristian Bush added. "And making that a hit on the radio. That's something that wouldn't have happened without everyone here."
"Stay" also earned Sugarland the song of the year award later in the evening.
2014: The Year in Fashion [PHOTOS]