Nelson was born in Evanston, Illinois. She graduated with a degree in music from St. Olaf College in Northfield, Minnesota in 1961. On August 5 of the same year she married Alan H. Nelson, with whom she moved to Berkeley, California.

In Paris, Nelson joined the Five Centuries Ensemble, then in 1976 she was a founding member, with William Christie, and Wieland Kuijken, of René Jacobs’ Concerto Vocale, the chamber music ensemble which preceded Christie’s own Les Arts Florissants in 1979. She also performed with Christopher Hogwood’s Academy of Ancient Music, and Anthony Rooley’s Consort of Musicke – in soprano duets together with Emma Kirkby. Later she was one of the founding members of Nicholas McGegan’s San Francisco-based Philharmonia Baroque Orchestra, specialising in Handel and Purcell.

In opera she made her debut in Brussels in 1979, in Monteverdi’s L’incoronazione di Poppea under Alan Curtis. She was soprano for Christopher Hogwood’s landmark January 1982 recording of Handel’s Messiah, recorded in Westminster Abbey and videotaped by the BBC.