The result left the Albanians in third place on 11 points from seven games, seven adrift of Portugal who qualified for next year's tournament in France with a 1-0 win over Denmark.
The Danes are second on 12 points from eight games and have finished their campaign, meaning Albania can leapfrog them and qualify by winning their last match away to Armenia on Sunday.
Serbia left back Aleksandar Kolarov and forward Adem Ljajic scored stoppage time goals to silence a vociferous but well-behaved 13,000 home crowd in the central city of Elbasan.
Albania's Italian coach Gianni De Biasi said: "We played a very good match technically but made mistakes because it seemed to me the team was influenced by the fans.
"We should have taken a point but, just like against Portugal (in last month's 1-0 home defeat), we conceded in the last few minutes. I love that the players have a big heart but in some moments we should use logic," he added.
Serbia played with more purpose in the first half, with captain Branislav Ivanovic missing their best opportunity after firing a volley from inside the area just over the bar.
Albania worked hard but they only threatened Serbia with a stinging shot by Sokol Cikalleshi in the 76th minute.
When the game appeared to be heading for a stalemate, Albania lost concentration, just as they did in their last qualifier with Portugal, who they beat in their first game.
Ljajic set up Kolarov to score with an angled shot and put the icing on the cake for Serbia with a dink over goalkeeper Etrit Berisha after racing clear from inside his own half.
"This is a massive win despite the fact that we had lost any chance of qualifying. It can be the turning point for this team," captain Ivanovic told Serbian state television (RTS).
Albania's fans, apart from whistling the Serbia national anthem and booing several players, did not cause the trouble that marred the first match in Belgrade a year ago, which was abandoned, and even applauded the sportsmanship on the pitch.
(Reporting by Benet Koleka, Additional reporting by Zoran Milosavljevic; editing by Ken Ferris)
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