A superb volley by Dennis Rommedahl just before the half-hour mark had given the dominant Danes the lead but Norway's Bari forward Huseklepp outmuscled Michael Silberbaeur to slot home an equaliser after 81 minutes.
The home side created few clear-cut chances and, with striker John Carew missing due to a back injury, their best efforts came from set-pieces as 194cm tall centre-back Brede Hangeland caused plenty of problems for the Danish defence.
Denmark had settled well despite the best efforts of the direct and robust Norwegians to disrupt them, with promising Ajax Amsterdam winger Christian Eriksen excelling again.
Having given Denmark the lead in the 27th minute, Rommedahl had a chance to put the game beyond Norway's reach in the 73rd but this time he clipped the top of the bar after another clearance found him free on the edge of the box.
Eight minutes later Huskelepp made no mistake as he ran on to a through ball and finished left-footed past Thomas Sorensen.
Striker Niklas Bendtner had shaken off an ankle injury sustained in training to make the team lineup but was well-shackled on the night by Hangeland.
The draw means Norway have 10 points ahead of Portugal and Denmark on seven with all the teams in the group having played four games after Cyprus and Iceland drew 0-0 in in Nicosia.
Norway travel to Portugal for their next qualifier on June 4 when Denmark visit bottom side Iceland.
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