The two-time champions scored all four of their spot kicks to emerge triumphant after the match had ended 1-1 following extra-time.
Trine Ronning was the Norwegian hero, firing home the all-important penalty after Line Roddik and Theresa Nielsen missed for the Danes.
Norway had looked on course to secure victory in normal time when Marit Christensen bundled home a third minute corner.
However, Denmark fought back and forced extra-time when Mariann Knudsen nodded in on 87 minutes.
Both sides had chances to win it in extra-time, but it wasn't to be, and Norway ultimately prevailed on penalties.
Even Pellerud's side will now face holders Germany in Sunday's final at the Friends Arena in Solna.
Norway made a super-charged start to the match and took the lead on three minutes when Christensen got the final touch on a left-wing corner.
Denmark responded with some neat possession play, but it was the Norwegians who carved out the better opportunities with Solveig Gulbrandsen going close to doubling the advantage with a header from another set piece.
Ada Hegerberg then came within a whisker of netting a contender for goal of the tournament with an audacious turn and shot that cannoned back off the upright.
Denmark looked sharper after the interval and Knudsen twice went close to levelling with a low shot that arrowed inches past the post and a header that she somehow failed to convert.
Norway remained a threat on the counter attack and Caroline Hansen was thwarted by a brilliant save from Stina Petersen.
The Danes continued to press late on and finally drew level with just two minutes left when Knudsen headed in from six yards out after a long free-kick was diverted into her path.
The pattern of play continued in extra-time but it was Norway who had the best chance to win it when Petersen produced a sensational one-handed stop to keep out substitute Elise Thorsnes' goalbound shot.
Norway then held on to force spot-kicks and booked their place in the final courtesy of four well-struck efforts.