The track is also the only song by a group in the Alternative Songs top five.
Of Monsters and Men's "Alligator" crowns Billboard's all-rock-format Rock Airplay chart, surging 4-1 on the Aug. 24-dated list.
The lead single from the Icelandic rockers' new album, Fever Dream, earned 8.8 million audience impressions, up 9%, according to Nielsen Music.
The song is Of Monsters and Men's first Rock Airplay leader, after the act reached a prior No. 2 best with "Mountain Sound" in 2013. The band also boasts a No. 3 hit in its 2012 breakout single "Little Talks."
Of Monsters and Men becomes the second act to earn its first Rock Airplay leader in 2019, following Shaed, whose "Trampoline" led for three weeks beginning in July.
"Alligator" now has ruled two airplay rankings, having topped Adult Alternative Songs for two weeks in July.
The track concurrently leaps 6-3 on Alternative Songs, where it's the only title by a group in the top five amid a trend toward more solo success at the format.
Fever Dream, Of Monsters and Men's third studio album and first since 2015's Beneath the Skin, debuted at No. 1 on Top Rock Albums and No. 9 on the Billboard 200 dated Aug. 10.