Ibrahimovic then sealed the win in the 86th when substitute Kim Kallstrom found him with a long ball into the area. The Sweden captain controlled the ball with one touch and then slotted a low shot into the far corner with his second.
"It's magical," Ibrahimovic said. "It was a fantastic feeling. Now we're one step closer to the World Cup."
However, Ibrahimovic will be suspended against Germany after a late booking in the final minutes.