Rice, better known as a diplomat and national security adviser, is also a classically trained pianist.
Their appearance in the three-hour concert before an estimated crowd of 8,000 overflowed with Franklin's catalog of hits and arias from the world of opera and classical music.
Rice played piano while Franklin sang her hit "I Say A Little Prayer" as well as "My Country 'Tis of Thee."
Earlier in the program, Rice performed a selection from Mozart's Piano Concerto No. 20 in D Minor with the orchestra, a piece she said she practiced furiously.
The two met at a White House function.
The Associated Press contributed to this report.