Russia took the lead on the half-hour against the run of play when midfielder Alexander Samedov pounced on the rebound after keeper Vladimir Stojkovic could only parry Roman Shirokov's shot from the edge of the area.
The Serbians, who failed to qualify for the World Cup to be held in Brazil in June, levelled two minutes later as Filip Djordjevic headed in a left-wing cross from Dusan Tadic.
Capello's side upped the tempo in the second half and Alexander Kokorin missed two good scoring opportunities.
Serbia, for their part, always looked a threat on the counter-attack.
Capello employed a 4-5-1 formation featuring two wide players in midfield and a lone striker in Alexander Kokorin who only joined the squad in Dubai on Thursday after losing his passport.
Russia also play South Korea, ranked 56th in the world, at the same venue on Tuesday.