The Kazakh pair converted their first match point when Wawrinka could not control Golubev's powerful return of Federer's serve.
"Against those guys you have to play almost the perfect match. I'm happy that we did today," Golubev said.
Federer and Wawrinka, the Australian Open champion, won gold in doubles at the 2008 Beijing Olympics and were loudly supported by the 16,000 spectators in the indoor Palexpo arena.
"Pretty excited, especially that we beat the Olympic champions. It makes it special," said Nedovyesov, who is ranked No. 76 in singles.
In Sunday's reverse singles, No 3-ranked Wawrinka is scheduled to play the 56th-ranked Mikhail Kukushkin before Federer takes on the 64th-ranked Golubev, who beat Wawrinka in Friday's opening singles.