Zlatan Ibrahimovic scored his ninth goal of the Euro 2016 qualifying campaign for Sweden, but Denmark scored a late away goal in the first leg of their playoff encounter.
Paris St Germain forward Ibrahimovic continued his rich vein of form by converting a second-half penalty after Emil Forsberg had opened the scoring for the Swedes in the first period of the all-Scandinavian affair.
However, it would finish 2-1 as Nicolai Jorgensen stabbed in from close range from Christian Eriksen's corner to raise Danish hopes ahead of Tuesday's return fixture.
And the Swedes only need to look at their most recent play-off contests to know they cannot solely rely on goals from their talisman, with Ibrahimovic's brace in a play-off for the World Cup finals in 2014 counting for little when he was upstaged by Cristiano Ronaldo's hat-trick.
Early on it looked like Sweden were going to rue a series of first-half chances spurned by Marcus Berg.
Kasper Schmeichel denied him at first with a smart reaction stop from a near-post effort from Oscar Lewicki's ring-wing centre, but the Panathinaikos forward failed to even hit the target with his next three tries.
The first was a header over from a corner and he was stretching to reach the second that he poked wide, yet the third was a brilliant opportunity that the striker should have hit the target from.
Ibrahimovic flicked the ball over Daniel Agger, setting Berg free in the area, and his shot across goal was pulled harmlessly wide.
Denmark, who had started in lively fashion, almost made Berg play when Eriksen's chipped pass found Nicklas Bendtner and the ex-Arsenal forward's side-footed volley went wide while his shirt was being held by substitute Erik Johansson.
The Swedes then broke the deadlock in the 45th minute courtesy of a fine first-time finish from Forsberg.
Jimmy Durmaz's back heel released Mikael Lustig down the right flank and he pulled a low cross into Forsberg, who swept a first-time shot into Schmeichel's far corner.
The Leicester stopper was powerless to prevent that attempt but he made a terrific stop to deny Ibrahimovic making it 2-0 with the final kick of the half.
The PSG striker won a free-kick on the edge of the area as he hurdled Agger, who was booked for his troubles, and he smashed the set piece towards the top corner only to see Schmeichel brilliantly turn it around the post with his left palm.
The two would meet again in another set-piece scenario five minutes after the interval.
Forsberg was involved again, dribbling into the box before Thomas Kahlenberg barged into his back and tripped him with a tangle of legs.
Referee Nicola Rizzoli awarded the penalty and although Schmeichel guessed the right way, Ibrahimovic's effort was fired right into the bottom-left corner for his 12th goal in his past dozen games for club and country.
He had the ball in the net again shortly afterwards too but was correctly ruled offside.
The visitors were asking few questions of the Swedish defence until the introduction of Jorgensen and Yussuf Poulsen turned the tide.
It was Poulsen who flicked a header from Eriksen on to Jorgensen for the Danish goal and the scorer almost grabbed an equaliser when heading over as Swedish nerves kicked in.
They avoided conceding again, yet Jorgensen's first goal for his country left the tie in the balance.