Hungary, in third place, cannot now catch the Swedes who have a better head-to-head record.
An early goal by Sebastian Larsson put the visitors in front but a young Finnish side pressed hard in the pouring Helsinki rain and controlled the first half without threatening keeper Andreas Isaksson's goal.
"I am very happy. Finland played better than us today. We were effective and we won," Sweden coach Erik Hamren told reporters.
"It was cheap. He [the referee] apologised to me and said he was wrong," said Ibrahimovic.
The winners of Europe's nine qualifying groups and the best second-placed team gain automatic berths in the finals alongside joint hosts Poland and Ukraine while the other eight runners-up enter two-legged play-offs for the remaining four places.
