Norway held off a second-half fightback by Cyprus to make it nine points from nine at the top of group H.
John Arne Riise's early goal and John Carew's calm finish shortly before the interval appeared to have put the Scandinavian side in control.
But Yiannis Okkas put the match back in the balance and Norway keeper Jon Knudsen was to the fore as his side were forced to defend strongly.
Norway were ahead after only 84 seconds as Riise finished off a break led by fellow-full-back Tom Hogli. Hogli found Erik Huseklepp and the winger squared the ball for Riise to run onto the ball and finish low past keeper Antonis Georgallides.
And the visitors went close to a second when Bjorn Helge Riise, brother of the goalscorer, delivered a corner which was missed by Georgallides but Huseklepp's header was cleared off the line.
Cyprus had an opportunity to equalise six minutes before the interval but Mihalis Konstantinou headed Efstathios Aloneftis' cross over.
And he was made to pay three minutes later when Carew beat two defenders including his marker Elias Charalambous and slotted the ball into the bottom corner.
Cyprus' Andreas Avraam had the first chance of the second period but was forced wide and Jon Knudsen saved his shot.
The hosts continued to have the better of the half, though, and Okkas cut the deficit shortly before the hour mark. Constantinos Makridis seized on John Arne Riise's hesitation and teed up Okkas to tap home from close range.
Carew's volley from Bjorn Helge Riise's cross was tipped around the post by Georgallides but Cyprus went close to an equaliser when Aloneftis' effort was cleared off the line by Norway captain Brede Hangeland.
Knudsen then made an excellent save to deny the same player the equaliser Cyprus possibly deserved.