Bilan received 272 points from telephone voters in 43 countries.
Ukraine came second and Greece third.
Sweden had been tipped as favourites at the start of the contest finale in the Serbian capital, watched by an estimated 100 million television viewers worldwide.
Serbian singer Marija Serifovic won last year's competition with her ballad "Molitva," or "Prayer", bringing the competition this year to Belgrade - for the first time.
Serifovic opened the final evening at Belgrade's biggest Arena sports hall.
|Sweden, represented by Perrelli, were one of|
the favourites at the contest's start [AFP]
Other guest stars include Bosnian ethno musician Goran Bregovic and Serbia's NBA star, Vlade Divac.
The first of the 25 finalists to perform was the Romanian duo Niko & Vlad, with a love ballad, followed by Britain's Andy Abraham.
Though criticised by many as a show of kitsch and an extravaganza, the Eurovision Song Contest, or Eurosong, is revered by its many followers.
They often travel across the continent to support their favourite singers.
About 15,000 guests we believed to have arrived in Belgrade for the event.
Serbia is still deciding on how and when to join the European Union following elections on May 11, with the main parties engaged in coalition negotiations that could keep the country outside the bloc.
On Saturday evening, a huge screen was put up in front of Belgrade's City Hall.
Fireworks marked the competition's end.
The finale included 20 contestants who made it through the two semifinals earlier this week.
In addition, contestants from the UK, France, Germany, Spain and Serbia, the host country, will go straight into the final without having competed in preliminary rounds.
Observers in past have complained of so-called bloc-voting among Balkan, Baltic and Scandinavian states. This year was not particularly different.