Ermir Lenjani has given Albania a surprise 1-0 half-time lead over Denmark after the Scandinavians wasted several chances to score before the break in Tirana.
The Danes, searching for a second win of their Euro 2016 qualifying campaign after beating Armenia in their opening game, were almost ahead early on when Simon Kjaer's header from Michael Krohn-Dehli's cross was saved by Etrit Berisha.
Morten Olsen's side had further chances to edge in front with both Christian Eriksen and Yussuf Poulsen missing the target for the visitors.
Tottenham Hotspur playmaker Eriksen then set up another opportunity for Kjaer, but this time the central defender was unable to test the Albanian keeper.
The hosts then had their first opening when Andi Lila met Lenjani's cross, only to see his header drift over Kasper Schmeichel's goal.
Albania looked a greater threat as the half progressed and Taulant Xhaka was denied by the Leicester City stopper, who needed to make a solid save to keep Denmark level.
The home side were to grab a half-time lead, though, as Lenjani rounded off a fast counter-attack on 38 minutes with a long-range shot that Schmeichel was unable to keep out.
