Bopanna and his Dutch partner Matwe Middelkoop, seeded ninth, were stunned by the unseeded Italian pair of Andrea Vavassori and Lorenzo Sonego
Divij Sharan and his Serbian partner Nikola Cacic fought hard before going down in three sets
Sania Mirza and Rajeev Ram needed an hour and 27 minutes to defeat the Dutch-Aussie pair of Ellen Perez and Matwe Middelkoop 7-6(4), 6-4.
Experienced Indian Rohan Bopanna and his Canadian partner Denis Shapovalo advanced to the second round of the US Open men's doubles event after a straight-set win in New York.
Bopanna and Shapovalov will take on Dutch-Romanian combination of Jeal-Julien Rojer and Horia Tecau in the quarterfinals.
Mirza, who will retire after the 2022 season, served well in the contest.
Nagal's court coverage and solid defence in long drawn points was the highlight of his win.
Serbia had their backs to the wall when Kazakh veteran Mikhail Kukushkin beat debutant Miomir Kecmanovic in a three-hour epic in the first singles rubber. But Djokovic calmly levelled the tie with a straight-sets defeat of Alexander Bublik before returning to court to team up with Nikola Cacic and beat Kazakh pair Andrey Golubev and Aleksandr Nedovyesov 6-2, 2-6, 6-3.
World number one Novak Djokovic overpowered Dennis Novak after Dusan Lajovic battled past Gerald Melzer and Serbia went on to a 3-0 win in their opener against Group F hosts Austria in the Davis Cup Finals in Innsbruck on Friday.
The winners of the Serbia-Germany tie will join Spain, Russia and Italy in the semi-finals.
Favourites Russia Tennis Federation opened their Davis Cup Finals campaign with a resounding victory over Ecuador, Britain began with a win against France and Italy eased into the quarter-finals with a win over Colombia on Saturday.