The British boy band took on the US group's 1999 track during the Swedish leg of their 'Take Me Home' tour, impressing the elder band's Howie Dorough.
He told MTV News: ''I think they did a good job on it. One of the writers, that's written almost all their big stuff, Rami Yacoub, he worked with us in the early days with Max Martin and stuff like that, some of the biggest songs of ours.
''The sound that they've originated was definitely not too far from where it came, from the same Swedish camp.
''I think they did a great job. It seemed like it went over really well.''
Howie was particularly impressed to see One Direction's version of the song - performed by singers Niall Horan, Harry Styles, Zayn Malik, Louis Tomlinson and Liam Payne - become talking point for almost a week.
He added: ''I get Backstreet Boys Google [Alerts] every day and it seemed like it was there for three or four days.''