Serbia had initially been awarded a 3-0 walkover by UEFA because the drone carried a pro-Albania flag but they were still deducted three points and ordered to play their next two qualifiers in an empty stadium.
However, CAS has decided that since Albania did not refuse to play on in a hostile atmosphere in Belgrade it was Serbia who were responsible for the game not being completed.
“The panel found that the match stoppage and the eventual abandonment of the match were caused by security lapses of the organisers and acts of violence exerted on the Albanian players by the Serbian fans and at least one security steward,” CAS said in a statement.
“As such, the panel holds that the Football Association of Serbia and not the Football Association of Albania must be considered as responsible for the match not being played in full.”
Nevertheless, the Albania FA (FAA) will still have to pay a 100,000 euros (72,106 pounds) fine after CAS agreed with European football’s governing body UEFA that “the FAA was responsible for the drone operated during the match”.
Albania are now level on 10 points with second-placed Denmark in Group I, two points behind leaders Portugal.
Serbia are bottom with minus two points.
The Group I game was interrupted when a flag depicting so-called Greater Albania, an area covering all parts of the Balkans where ethnic Albanians live, was flown over the terraces and pitch by a remote controlled mini drone.
A Serbian player eventually grabbed the flag at the Partizan stadium, prompting an angry reaction from Albanian players and an unsightly melee ensued.
Security was tight for a game with no away fans allowed which was held against the backdrop of long-running Serb-Albanian tensions over Kosovo, a majority-Albanian former Serbian province that declared independence in 2008.
NATO waged a 78-day air war in 1999 to halt the killing and expulsion of ethnic Albanians in Kosovo by Serbian forces fighting a two-year counter-insurgency war. Serbia does not recognise Kosovo as independent.
The return match is due to be held in Albania on Oct. 8.
(Reporting by Michael Hann; editing by Ken Ferris)