"It's magical," Ibrahimovic told Swedish TV after the game.
"It's a fantastic feeling. We are a step closer to the World Cup.
"With the support we had today, a sold-out arena, it doesn't get any better."
Ibrahimovic has now scored 10 of Sweden's 14 goals at their new national stadium, the Friends Arena.
"The whole team should get credit, not only me, because we came out totally different in the second half," he said.
Germany head the group with 25 points going into the final round of qualifiers on Tuesday. Sweden have 20 points and will go into the play-offs for a place in Brazil next year. Austria are third with 14 points.
Ibrahimovic's side had to dig deep to come from behind after the visitors took a 29th-minute lead.
Johan Elmander hit the post for Sweden before half-time but it was a different story after the break as Ibrahimovic began to exert a strong influence.
The home side levelled in the 56th minute, left back Martin Olsson meeting Ibrahimovic's deft chip with a diving header.
Sweden continued to threaten, Olsson firing a left-footed drive just over as they pressed for a winner.
For all his industry, Ibrahimovic had few clear chances himself, spurning the best of them by shooting straight at the keeper midway through the second half.
But when Kallstrom played him in with four minutes remaining, he made no mistake.
Arnautovic was sent off for appearing to head-butt Elmander in the closing moments and David Alaba had a chance to equalise but screwed his free kick narrowly wide.
Ibrahimovic will miss Sweden's final game of the qualifying campaign, at home to Germany on Tuesday, after picking up a late yellow card.