Nani gave the visitors an early lead and substitute Joao Moutinho sealed their win after Zoran Tosic equalised for the Serbians, who had Aleksandar Kolarov and Nemanja Matic sent off for dissent in the closing stages.
A seventh successive win left Portugal top of the section with 21 points from eight games, seven more than second-placed Albania who joined them in next year's tournament with a 3-0 win at Armenia.
Third-placed Denmark, who have 12 points, are headed for the playoffs, with Serbia finishing fourth on four points ahead of the Armenians with two.
The visitors took an early lead on a cold and rainy night when Nani swept a rebound into the top right corner after Serbia keeper Vladimir Stojkovic could only parry a low shot by Danny.
The home said had the upper hand and missed a string of chances in either half, with forward Adem Ljajic forcing a fine save from Rui Patricio in the 38th minute.
Tosic finally rewarded their hard work midway through the second half, drilling a fierce shot into the roof of the net from 10 metres after a darting run and cross from the left by Aleksandar Kolarov.
Moutinho netted a superb winner in the 78th minute, beating Stojkovic with a curling shot from 25 metres before Kolarov and Matic were sent off in quick succession for lashing out at opponents as tempers flared.
Stojkovic kept out a stinging shot by Nani before some last-gasp defending by the visitors denied nine-man Serbia a share of the spoils in the final few minutes.
(Editing by Mike Collett)
