Portugal, held to a frantic 4-4 draw at home to Cyprus in their Group H opener, fell behind in Oslo when Erik Huseklepp put the ball into an empty net after John Carew had blocked a clearance by Portuguese goalie Eduardo.
Missing the injured Cristiano Ronaldo, Portugal could not find the creativity needed to break through a stubborn Norway defence, anchored by Brede Hangeland.
Norway, who failed to qualify for the 2008 European championships or this year's World Cup, top Group H with six points from two games. Portugal are stuck on one point after two games.
"We won a great defensive battle," coach Egil Olsen said. "The win was not entirely undeserved if you ask me, we didn't create much but had good control in the back."
Norway, who beat Iceland 2-1 last week, tightly marked Manchester United's fleet-footed winger Nani, limiting Portugal to shots from long range for much of the match.
"Norway is an outsider, normally Portugal and Denmark would be the strongest teams. We have six games left and we can still qualify," Oliveira told reporters.
