Austria's David Alaba put his side in the lead, before Sweden midfielder Erkan Zengin scored his first international goal to put Sweden level.
Star striker Zlatan Ibrahimovic reached his 100th cap, after becoming Sweden's all time record goal scorer last Thursday in an international friendly against Estonia.
But he was well marked by the Austria defense on Monday's game and never came close to scoring. He was also booked in the first half after hitting Alaba with his elbow and roughly tackling Martin Harnik.
"You saw another side of Zlatan today because he was working really hard for the team," Sweden coach Erik Hamren said.
"I am happy with the result, I am also happy with the game … I am sure it's going to be a really important point in qualifying."
The stalemate means the Swedes have still never won in Austria but having been beaten 2-1 on their last outing, coach Erik Hamren will be happy to have gained a point from one of the tougher away games his side face in qualifying.
Also in Group G, Russia downed Liechtenstein 4-0 to lead after the opening round, and Montenegro beat Moldova 2-0.