Chris Iwelumo, making his international debut as a second-half substitute, was the villain of the piece as he missed a golden chance to give the Scots a lead from just two yards out.
Despite some late pressure the Scots could not find a way past the Norwegian defence and the draw leaves them struggling to qualify for South Africa 2010 just three games into their Group Nine campaign.
"We couldn't quite get that goal," said coach George Burley. "I thought in the second half that we put them under alot of pressure. It wasn't working for us in the first half with one up front, so we decided to change."
On Iwelumo's miss, Burley said: "It was just one of those things. I don't know whether he miss-hit it or was a bit flat-footed. One thing is for sure: it was the best chance of the game. They had chances but that was because we were pushing up."
Their first effort on target came after eight minutes. West Brom's James Morrison was played into the box by Kirk Broadfoot but his shot was straight at Jon Knudsen.
But Norway soon settled into the game and giant Aston Villa striker John Carew was giving the Scottish defenders all sorts of problems. In the ninth minute he powered through the centre of the Scottish defence and only a last ditch tackle from Gary Caldwell deflected his shot wide of Craig Gordon's post.
Ten minutes later Carew outpaced Caldwell down the left wing and fired in a shot at Gordon who palmed it into the path of Bjorn Helge Riise but he blasted the rebound over the bar.
In the 22nd minute Morrison went on a good run down the right wing but his cross was just behind lone striker James McFadden.
David Weir came to Scotland's rescue after 40 minutes when he did enough to smother a Carew shot to allow Gordon to collect after a header across goal by Fredrik Stromstad.
In the final minute of the half a McFadden cross found Morrison at the back post but he headed his effort over the bar.
In the second-half Carew picked up where he had left off and had two chances to give Norway the lead within the first five minutes but both his efforts were straight at Gordon.
Kjetil Waehler should have given Norway the lead in the 54th minute when he was found unmarked at the back post but he headed his effort into the side netting.
Knudsen did well to hold on to a powerful strike from Barry Robson who unleashed a powerful first-time strike from the edge of the box after 55 minutes.
Best chance gone
Substitute Iwelumo, on for fan favourite McFaddden, spectacularly missed a golden chance to put the Scots ahead in the 64th minute. The Wolves striker knocked the ball past the post when all he had to do was tap it into the open goal from two yards out following Gary Naysmith's inch-perfect cross.
Scotland pushed forward looking for the opening goal and Shaun Maloney was involved in two good chances.
In the 73rd minute he beat two defenders on the left wing before cutting in and firing a rocket shot past Knudsen's post. Then two minutes later his low drive was deflected wide after he collected an Iwelumo knockdown in the box.
The Scots were relieved to see Waehler's diving header go wide of the post in the 80th minute after he was found unmarked in the box from a corner.
Scotland had keeper Gordon to thank for saving them in the 85th minute when he blocked a powerful Steffen Iversen volley from six yards out.
As the Scots pushed for a winner gaps appeared in defence and Carew should have sealed all three points for Norway when he was one-on-one with Gordon but he chipped his shot over the bar.
In the final minute both Iwelumo and fellow sub Steven Fletcher just failed to connect with a Broadfoot cross as the Norwegians held on for a draw.