In 1975 Moore signed with Buddah Records and released the critically successful R&B album, Peach Melba, which included the minor hit, "I Am His Lady". The following year she scored her first significant hit with the Van McCoy-penned "This Is It", which reached the Billboard Hot 100, the top-20 position on the R&B chart, and top-10 in the UK, becoming her biggest success in that country. 'This is It' also became the number 1 disco track in the UK for that year. It would be 18 years later that Australian singer Dannii Minogue will cover this song and make it to number 10 on the ARIA charts.
In 1976 she scored her third Grammy nomination with the R&B ballad "Lean on Me", which had been recorded originally by Vivian Reed and later by Moore's idol Aretha Franklin who recorded the song as a B-side to her 1971 hit "Spanish Harlem". The song is most notable for Moore's extended long note at the end. In 1983 she re-recorded the song as a tribute to McCoy, who had died four years earlier. Throughout the rest of the 1970s, Moore struggled to match the success of "This Is It" with minor R&B/dance hits. However, her hit 'Pick me up I'll dance' released in May 1979 produced by McFadden & Whitehead and released on Epic Records did have considerable UK disco success, reaching UK chart position 48, along with a further hit that same year, also produced by McFadden & Whitehead with a cover version of the Bee Gees' hit "You Stepped Into My Life", which reached the top 20 on the R&B charts and 47 on the Billboard Hot 100.
In 1981 Moore signed with Capitol Records and reached the top 5 on the R&B charts with the dance-pop/funk single "Love's Comin' At Ya", which also hit the top 20 in the UK (on EMI America EA 146) and became a sizable hit in some European countries for its post-disco sound and followed by "Mind Up Tonight", which was another top 40 hit in the UK reaching position number 22. A string of R&B hits followed, including 1983's "Keepin' My Lover Satisfied" and "Love Me Right", 1984's "Livin' For Your Love", 1985's "Read My Lips"—which later won Moore a fourth Grammy nomination for Best Female Rock Vocal Performance, making her just the third black artist after Donna Summer and Michael Jackson to be nominated in the rock category—and 1985's "When You Love Me Like This".