He is noted for being one the key figures in the development of the Motown label in Detroit, Michigan: his doo-wop group gave Marvin Gaye his start in his career, and he and his wife at the time, Gwen Gordy, distributed the very first Motown hit single, Barrett Strong's "Money (That's What I Want)", on their record label, Anna Records. Fuqua later sold Anna Records to Gwen's brother Berry Gordy, and became a songwriter and executive at Motown.
Mentored by Alan Freed, the group’s doo-wop harmony style achieved great success on the national R&B charts in the mid 1950s. Recording on Chess Records, Fuqua initially shared lead vocals with Lester, but eventually asserted himself as the leader of the group. This changed in 1957 when he, in effect, sacked the other members and installed a new group, previously known as the Marquees, which included Marvin Gaye. The new group, billed as Harvey and the Moonglows, had immediate further success, but Fuqua left in 1958. The Moonglows reunited temporarily in 1972, and in 2000 were inducted into the Rock and Roll Hall of Fame.
Fuqua left the Moonglows when Leonard Chess suggested that he join Anna Records in Detroit. At Anna Records, Fuqua began working with Anna Gordy, Billy Davis, Lamont Dozier and Johnny Bristol. He also introduced Marvin Gaye to Anna’s brother, Berry Gordy, and married their sister Gwen Gordy. In 1961, he started his own labels, Tri-Phi Records and Harvey Records, whose acts included the Spinners, Junior Walker and Shorty Long. However, tiring of running a small independent label, Fuqua welcomed the opportunity to work at Motown, and was hired to head the label's Artist Development department as well as working as a producer. Fuqua brought the Spinners and Johnny Bristol to Motown, and co-produced several hits with Bristol. He was also responsible for bringing Tammi Terrell to the label, and for suggesting and producing her duets with Marvin Gaye, including "Ain’t No Mountain High Enough" and "Your Precious Love”.
Around 1971, Fuqua left Motown and signed a production deal with RCA Records, having success particularly with the band New Birth. He also discovered disco pioneer Sylvester, and "Two Tons O' Fun" (aka The Weather Girls), producing Sylvester's hit singles "Dance (Disco Heat)" and "You Make Me Feel (Mighty Real)" in 1978 as well as his album Stars in 1979. He also served as Smokey Robinson's road manager. In 1982 he reunited with Marvin Gaye to produce the singer's Midnight Love album which included the single "Sexual Healing". In 2000 he set up his own "Resurging Artist Records”, and has also acted as a trustee of The Rhythm and Blues Foundation.