Portugal midfielders Tiago, Joao Moutinho and Fabio Coentrao maintained a firm grip on the match and only when Serbia equalised through a brilliant goal by Nemanja Matic early in the second half did the visitors look likely to get a result.
Portugal struck after 10 minutes when stalwart defender Ricardo Carvalho glanced a well-placed header into the net from close range.
Midfielder Nemanja Matic was a bright spark for a subdued Serbian side that lacked creativity, with Chelsea right back Branislav Ivanovic struggling as a central defender and at fault for Carvahlo's goal.
Matic, playing on his old Benfica stamping ground to great effect, connected with a breathtaking left-foot scissor kick to make it 1-1 after 61 minutes.
But Portugal struck straight back through man-of-the-match Coentrao, who slid in Joao Moutinho's low cross at the far post to cap an energetic performance.
Portugal saw out the remaining minutes without any major scares, bringing on Ricardo Quaresma to keep the overworked Serbian defence pinned back as world player of the year Cristiano Ronaldo produced an unusually quiet performance.
"My side showed a lot of maturity, a lot of experience," said Portugal manager Fernando Santos, who hailed his side's superb workrate.
"It is not, however, age or identity that plays the most important role in our squad but the willingness to work hard for the results we want...
"This is a squad of players, which is prepared to work hard to satisfy its goals," he told reporters.
Serbia coach Radovan Curcic rued the soft goals his team conceded on his competitive debut.
"We let in the goals in the worst possible moments for us, especially the second after we had equalised and got back into the game," he said.
"A quick transition is Portugal's greatest strength and you're always going to be vulnerable when you chase the game against them."
Portugual head Group I after four matches by two points from Denmark and Albania.
(Reporting by Ed Osmond, additional reporting by Zoran Milosavljevic, ,editing by Mark Meadows)
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