Postiga pounced at the front post to poke in a Nani cross in the 53rd minute as Portugal took almost an hour to break down the visitor's resilient defense.
Both teams and Denmark are tied atop the group, but Portugal leads on points difference with three qualifying matches to go.
Portugal dictated the run of play but had a hard time breaking through Norway's defense, and looked to be running out of patience before Postiga stuck his leg out.
Cristiano Ronaldo made little impression as the Portuguese promised more than they delivered.
The Portuguese are fighting back from a poor start to their qualifying campaign when they took just one point from their first two matches.
Under coach Paulo Bento, who replaced Carlos Queiroz last September, Portugal has built a 5-1-1 record.
''This game was no less harder than we'd expected,'' Bento said. ''We managed to take control and keep control.''
Ronaldo, in a subdued performance, lined up for a 10th-minute free kick and forced goalkeeper Rune Jarstein to leap to his right to push the ball wide. Ronaldo rose above the Norwegian defense five minutes before halftime but headed straight at the keeper from short range in his only other serious threat.
Norway was in defensive mood and tried to break the deadlock with counterattacks, though it ran out of options in the second half.
Erik Huseklepp, who got the only goal in Norway's 1-0 win over Portugal in Oslo last September, forced goalkeeper Eduardo to dive sharply to his right to keep the ball out in the 17th. Morten Gamst Pedersen should have produced more when he burst down the right for a shot in the 24th.
Postiga forced Jarstein to dive low to his right to keep out a shot that was heading into the corner just after the restart.
The goal spurred the Portuguese, and Carlos Martins came close with a long-range chance five minutes later.
Portugal: Eduardo; Joao Pereira (Silvio, 63), Bruno Alves, Pepe, Fabio Coentrao; Carlos Martins (Ruben Micael, 69), Raul Meireles, Joao Moutinho; Nani (Silvestre Varela, 86), Helder Postiga, Cristiano Ronaldo.
Norway: Rune Jarstein; Tom Hogli, Brede Hangeland, Vadim Demidov, John Arrne Riise; Bjorn Helge Riise, Henning Hauger, Christian Grindheim, Morten Gamst Pedersen; Erik Huseklepp (Daniel Braaten, 74), John Carew (Mohammed Abdellaoue, 60).