Shaqiri, who earned rave reviews playing for the senior side in their 2-2 draw with England at Wembley in a Euro 2012 qualifier a week ago, netted three minutes after the break in Aalborg.
The FC Basel starlet had several pop-shots at goal from distance throughout the first half, but it was from closer range that he found the net, weaving past several Danish defenders before slotting the ball past keeper Mikkel Andersen.
The youngster is already said to have attracted interest from the likes of Manchester United, Aston Villa and Spanish side Villarreal, and his wonder goal is likely to have turned more heads.
Denmark, with a highly-rated teenager of their own in the form of forward Christian Eriksen in their side, wasted several late chances in the Group A clash.
Earlier in the day, Belarus had picked up all three points with a 2-0 win over Iceland in the opening game with two late goals after Iceland's Aron Gunnarsson was sent off for a foul in the area.
Andrei Voronkov converted the spot kick in the 77th minute and Maksim Skavysh added a second 10 minutes later in Aarhus.
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