The Court of Arbitration for Sport (CAS) on Friday rejected an appeal by Serbia and awarded Albania a 3-0 win after the incidents that marred their Euro 2016 qualifier in Belgrade in October.
European football's governing body UEFA initially awarded Serbia a 3-0 win but also docked them three points in the wake of a match that was halted when irate home fans invaded the pitch and attacked Albania players after a pro-Albanian flag was flown over the stadium by a drone.
The Football Associations of both countries appealed against UEFA's decision at a hearing in April and the CAS confirmed on Friday that they had "partially upheld" the Albanian appeal while holding the Serbian FA responsible for the match not being played in full, therefore handing Albania a 3-0 win.
However, a fine of 100,000 euros (£72,123, $112,072) imposed on the Albanian FA will stand after CAS accepted they were responsible for the drone.
Meanwhile, CAS upheld all UEFA's punishments against Serbia, deducting them three points, ordering them to play their next two UEFA home games behind closed doors and fining them 100,000 euros.
The match, for which Albanian fans had been barred on UEFA's request, was goalless when it was abandoned in the 41st minute as Albania players fled to the changing rooms with chairs and other paraphernalia being thrown at them.
UEFA found that the Albanians had refused to play following an order issued by the referee.
But in a statement, a CAS panel said it was "unable to ascertain to its comfortable satisfaction that the referee issued a clear, direct and unconditional order to the players to resume the match on the basis of a definite decision that safety had been assured.
"The Panel found that the match stoppage and the eventual abandonment of the match were caused by security lapses of the organizers and acts of violence exerted on the Albanian players by the Serbian fans and at least one security steward."
Albanian officials hailed the CAS decision, with the Prime Minister Edi Rama writing on his Facebook profile: "That is European justice! 3 points for the Red-and-Black National Team in Belgrade!!!"
In Belgrade, Serbian Football Association (FSS) released a statement saying the ruling was "a precedent, we dare to say a shame for law and justice, politically coloured and scandalous for European and world football."
The FSS said it would consider a possibility to lodge an appeal to Swiss Federal court.
The two nations are in Euro 2016 qualifying Group I, with Serbia on just one point from five games and Albania, now with 10 points from four games, level with second-placed Denmark as they look to reach a major tournament finals for the first time.
Albania next play Denmark in Copenhagen in September, while Serbia will entertain Armenia behind closed doors in Novi Sad.