"Missionary Man", a US Top 20 hit in 1986, was performed by which band?

"Missionary Man" is a song by the Eurythmics, consisting of Annie Lennox and David A. Stewart. It peaked at #14 on the Billboard Hot 100 for the week ending October 11th, 1986. It was the only Top 40 single from their album, "Revenge", and inspired by Annie Lennox's brief marriage to a Hare Krishna.

Although not one of their signature songs, "Missionary Man" indeed won a Grammy for Best Rock Performance by a Duo or Group with Vocal, and the music video was played heavily on MTV, being nominated five times at the 1987 MTV Video Music Awards.