By 1980, D'Rivera had been dissatisfied with the constraints placed on his music in Cuba for many years. In an interview with ReasonTV, D'Rivera notes that the Cuban communist government described jazz and rock and roll as "imperialist" music that was officially discouraged in the 1960s and '70s, and that a meeting with Che Guevara sparked his desire to leave Cuba. In early 1981, while on tour in Spain, he sought asylum with the American Embassy, and left his homeland, wife and child behind in search of a better life with a promise to get them out.
Upon his arrival in the United States, D'Rivera found great support for him and his family. His mother Maura and his sister Rosario had left Cuba in 1968 and become US citizens. Maura had worked in the US in the fashion industry for many years, and Rosario was now a respected artist/entrepreneur . Many notables reached out to help Paquito, including Dizzy Gillespie, David Amram, Mario Bauzá and Bruce Lundvall, who gave him his first solo recording date. D'Rivera quickly earned respect among American jazz musicians and was introduced to the jazz scene at some of the most prestigious clubs and concert halls in New York. He became something of a phenomenon after the release of his first two solo albums,Paquito Blowin (June 1981) and Mariel (July 1982)