Ibrahimovic marked his first start in a competitive match for almost two months after injury by giving the visitors an early lead, but he later struck the post from a free-kick before Stevan Jovetic equalised from the penalty spot 10 minutes from time.
The PSG star had been a doubt for the game due to a persistent heel injury. The striker missed Sweden's previous qualifier victory against Liechtenstein and the 1-1 draw with Russia, both in October.
Sweden kicked off their Euro 2016 qualifying Group G with a 1-1 in Austria in September.
Austria retained their grip on Group G with a 1-0 win over Russia, a result which further increased the pressure on highly-paid coach Fabio Capello. The result comes a month after Russia were held at home by Moldova and days after the country's football union said they could no longer afford to pay Capello's huge salary, believed to be around €7 million ($8.8m) per year.
Austria are now four points clear at the top of the group from Sweden on six points, with Russia languishing in third on five points.
Elsewhere England and reigning champions Spain both secured home victories in Euro 2016 qualifying on Saturday as some of the continent's minnows again enjoyed outstanding results.
A turgid Group E encounter between England and Slovenia at Wembley came to life in the second half as Roy Hodgson's side fought back to win 3-1 and make it four wins from four games in Group E to remain firmly on track for a place at the finals in France.
Slovenia took the lead just before the hour mark when Jordan Henderson headed into his own net, but England were back on level terms moments later thanks to Wayne Rooney, who won and then converted a penalty to mark the occasion of his 100th international appearance with his 44th goal for his country.
Danny Welbeck of Arsenal then netted a brace to seal the victory.
"It was a good day in the end. We had to show character and that will be good for us in the team. Since the World Cup, we haven't faced that (going behind)," said Rooney, as England now turn their thoughts to Tuesday's friendly with Scotland in Glasgow.
Spain will go into a friendly with World Cup winners Germany fresh from a routine 3-0 victory against Belarus in Group C, a result that saw the current European champions make it three wins from four qualifiers.
Real Madrid midfielder Isco marked his first start for La Roja by scoring a brilliant first-half opener and Barcelona duo Sergio Busquets and Pedro Rodriguez added further goals in a game played in the southern town of Huelva.
"We played well, we dominated the match and scored twice in the first half which gave us a certain peace of mind," said Spain coach Vicente del Bosque.