Denmark scored two goals in the last two minutes to stun Portugal and snatch a 3-2 victory in Lisbon.
The hosts led through a 42nd-minute strike by Manchester United winger Nani until Arsenal's Nicklas Bendtner drew Denmark level eight minutes from time.
Carlos Queiroz's men looked to have ridden the storm when Chelsea playmaker Deco restored their lead with an 85th-minute penalty.
But Christian Poulsen and Daniel Jensen struck in the last two minutes of normal time to shock the home crowd and grab all three points.
That means Denmark are joint leaders of Group One on four points with Sweden and Albania, who both claimed home victories on Wednesday.
Sweden recorded a 2-1 win over Hungary after drawing 0-0 with Albania in their opening qualifier.
Kim Kallstrom broke the deadlock in the 55th minute before Samuel Holmen doubled Sweden's lead 10 minutes later, while substitute Gergely Rudolf gave Hungary a consolation at the death.
Albania enjoyed a 3-0 win over Malta with Erjon Bogdani scoring on the stroke of half-time before Klodian Duro and Armand Dallku struck in the last six minutes to clinch victory.