Cuba's Nivaldo Diaz and Sergio Gonzalez won in three sets, edging the hosts 24-22 in the first before stumbling 21-23 in the second and clinching the match 15-13 in the third.
Diaz and Gonzalez are the first men's beach volleyball team Cuba has fielded in an Olympics since the Athens Games in 2004.
The loss dismayed the pro-Brazil crowd on the sands of Copacabana, in a match punctuated by wild cheers for the home pair as the teams battled in a tit-for-tat match-up.
Solberg and Evandro were listed fourth in the International Volleyball Federation's June Provisional Olympic Ranking, while the Cuban pair were not ranked.
Brazilians have pinned their hopes at the Rio Games on re-establishing their dominance in the sport in which American challengers have grown increasingly successful.
Brazil's top-ranked team, Alison Cerutti and Bruno Schmidt, the 2015 world champions, won their first Pool A match on Saturday against Canada's Josh Binstock and Samuel Schachter.
(Reporting by Amy Tennery; Editing by Ken Ferris)
