The holders had to recover from going behind but secured all three points through goals from João Cancelo and Gonçalo Ramos, completing four wins from four in Group A4 and sealing their place in the quarter-finals.
Norway strike first
Norway stunned the home supporters by taking the lead in the 36th minute.
Kristoffer Ajer produced an excellent finish from outside the penalty area, sending a dipping half-volley beyond the Portugal goalkeeper to give the visitors a 1-0 advantage.
Portugal, however, responded almost immediately.
Cancelo restores parity
Just two minutes after Norway's opener, João Cancelo levelled the contest with a superb strike.
The Manchester City defender's effort from an angle flew into the net to make it 1-1 and give Portugal renewed momentum heading into the second half.
Ramos completes the comeback
Portugal continued to push for the winner after the interval and eventually found it in the 79th minute.
João Félix headed the ball across goal, allowing Gonçalo Ramos to get a decisive touch and send the ball into the net to put Portugal 2-1 ahead.
Norway were unable to find a second equaliser as Portugal held on to extend their 100 per cent record.
Conceição sent off late on
Portugal's victory was slightly soured in the closing stages when Francisco Conceição was shown a second yellow card and sent off.
The hosts nevertheless held on to secure their fourth consecutive Nations League victory.
Portugal qualify for quarter-finals
The victory moved Portugal to 12 points from four matches, six points clear of second-placed Denmark.
With a top-two finish now guaranteed, Portugal became the first nation to book their place in the Nations League quarter-finals.
The result is particularly significant because Portugal achieved it without Cristiano Ronaldo, who had left the national team camp following a dispute surrounding his omission from the starting line-up.
Match summary
• Portugal: João Cancelo 38', Gonçalo Ramos 79'
• Norway: Kristoffer Ajer 36'
Portugal will next face Denmark in November before concluding their Group A4 campaign away to Wales.