The Paris St Germain striker latched on to Kim Kallstrom's long ball and slotted the ball home with four minutes to go to make sure Sweden finished as runners-up to group winners Germany.
Earlier, Austria took a 29th-minute lead when Marko Arnautovic surged clear down the left and his cross was touched on by Marc Janko for Martin Harnik to thump the ball home.
Sweden levelled in the 56th minute, left back Martin Olsson meeting Ibrahimovic's deft chip with a diving header.
The Swedes (20 points) end their campaign against Germany (25) in Stockholm on Tuesday.
The home team started brightly and Fulham winger Alexander Kacaniklic twice went close in the opening minutes.
Austria, with Bayern Munich midfielder David Alaba pulling the strings, gradually eased their way back into the game and their lead was well deserved.
Johan Elmander hit the post for the Swedes before halftime but it was a different story in the second half as Ibrahimovic started to exert a strong influence.
(Editing by Tony Jimenez)
