Zlatan Ibrahimovic's first-half goal has given Sweden a 1-0 lead over Denmark as Erik Hamren's side have opened up a 3-1 aggregate advantage.
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Mikael Lustig almost headed into his own net inside the opening 10 minutes, but the defender's attempted clearance came back off the crossbar.
Denmark continued in the ascendancy as Yussuf Poulsen forced Andreas Isaksson into a save after a mazy run into the box.
However, Ibrahimovic slammed a half-volley into the back of the net from Kim Kallstrom's corner in the 19th minute to stun the home crowd into silence.
Kasper Schmeichel then made a sprawling save to prevent Ibrahimovic from doubling his tally before Daniel Agger was relieved to see his attempt at a block loop onto the top of the net.
Denmark could have made it 1-1 on the night just before half time, but Nicklas Bendtner couldn't direct Pierre-Emile Hojbjerg's cross on target.
