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.
Notable deaths of 2014 [PHOTOS]