Sweden ended a run of five winless games against Denmark, defeating them 2-1 in their Euro 2016 play-off first leg.
In a tight opening period here on Saturday, Denmark's Kasper Schmeichel was the busier of the goalkeepers.
Marcus Berg hoped his 18th-minute close-range effort would pay off, but Schmeichel stood firm.
Sweden went ahead through midfielder Emil Forsberg in the 45th minute.
Jimmy Durmaz combined nicely with Mikael Lustig down the right for Sweden, and the full-back's low cross was met expertly by Forsberg for his first international goal.
Sweden thereafter looked in control, with Denmark able to force little but the odd corner.
Their star striker Zlatan Ibrahimovic then converted A 50th-minute penalty to double the advantage.
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It looked to be all Sweden at that point onwards but Nicolai Jorgensen opened his international account with away goal with ten minutes to go to make the tie interesting.
Denmark pushed hard for an equaliser but the away goal nonetheless gives them hope for Tuesday's second leg.