Frank Sinatra and Sammy Davis Jr., and RUN-DMC and Aerosmith, being very far back on the stage -- not letting-themselves-go enough, and too goofy, respectively. Chaka Khan only does back-up vocals with Steve Winwood on "Higher Love". I'm thinking more of a Riggs and Murtaugh, Rocky and Apollo, Foley-Taggart-Rosewood kind of team result.
Heard the one below on the radio today, and it's got to be near the top of the list. (For those born within 5 years of 1980, you have also heard it in instrumental form in this video game music.) It's by Phil Collins (also with Genesis) and Philip Bailey (also with Earth, Wind, & Fire).