Fernando Santos' men took the lead after just 10 minutes at Estadio da Luz thanks to a header from veteran defender Ricardo Carvalho.
Carvalho was forced off soon after through injury, and Portugal looked set to be in for a frustrating night when Nemanja Matic equalised for Serbia.
Any grievances Portugal may have had were swiftly forgotten, however, as Coentrao netted what proved to be the decisive goal following a wonderful ball into the box from Joao Moutinho.
Serbia - competing in their first qualifier under Radovan Curcic - could not muster a late rally - as Portugal saw the game out to go two points clear of second-placed Denmark.
Carvalho broke the deadlock following a quick start from the hosts as he capitalised on poor Serbia defending to convert Coentrao's precise right-wing delivery.
However, just seven minutes later Carvalho was withdrawn from the action. The former Chelsea and Real Madrid man limped off to be replaced by Jose Fonte, making his competitive international debut.
Instances in which Serbia threatened the Portuguese goal were rare but striker Aleksandar Mitrovic should have done better when presented with a simple chance in the 52nd minute.
Mitrovic rose highest to meet Dusan Tadic's left-wing cross but could only direct his point-blank header over the frame of the goal.
His profligacy mattered little as Matic levelled in magnificent fashion, the midfielder turning home Radosav Petrovic's header across the box with a stunning bicycle kick at the far post.
Yet parity lasted all of two minutes for the visitors, with Coentrao tapping home a simple finish at the end of an excellent attack, following a demonstration of vision and accuracy from Moutinho.
