Goals from Filip Djordjevic, Aleksandar Kolarov and Lazar Markovic put the game beyond Wales, who never looked like avenging the 6-1 mauling they suffered at the hands of the same opponents in Novi Sad a year ago.
Gareth Bale, a pre-match doubt due to a groin problem, appeared just before the hour to get his first action since joining Real Madrid to become the world's most expensive player.
He almost scored a wonderful late free-kick, which was about as good as it got for the hosts as they suffered their sixth defeat from eight qualifying games.
The Dragons were booed off at the final whistle, but Coleman has no intention of stepping aside, and fully expects to sign the two-year contract extension he has agreed with the Football Association of Wales.
"I have every intention of leading this side into the next qualification campaign," he said.
"We have two wins out of eight, which is not good but I am still excited about the group we could have available.
"The next campaign will be a better one."
He added: "The contract has been agreed, although I have not signed it, but if I thought I could not affect this group of players I would not waste my country's time.
"We can do something special, with a fresh run at it.