Norway jumped onto the front foot from the first whistle, and they broke the deadlock in just the 13th minute when Tarik Elyounoussi found space inside the box to fire home from Per Ciljan Skjelbred's clever pass.
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The hosts dominated the exchanges for the majority of the first half, but were guilty of failing to capitalise as Martin Linnes struck an effort straight at Nikolay Mihaylov after beating the offside trap.
It would once again be the home side who took control early in the second half, but they were left frustrated when Joshua King's curled strike drifted just past the post.
The visitors continued to improve as the match progressed, and it looked like Bulgaria would find a winner as the game reached the latter stages.
However, the crucial third goal would be scored by Norway with 19 minutes remaining as Skjelbred curled another cross into the box, allowing Nielsen to drill home the winner.