Substitutes Federico Chiesa and Matteo Pessina netted in style on 95 and 105 minutes as Roberto Mancini's unusually labored side set up a meeting with Belgium or Portugal, who play Sunday. Sasa Kalajdzic's diving header made for a nervy final six minutes.
Italy's unbeaten record beats their previous best set in the 1930s under double World Cup-winning coach Vittorio Pozzo. They also beat former Italy goalkeeper Dino Zoff's record of not conceding in 1,143 minutes between 1972 and 1974.
Kalajdzic's late extra-time goal was the first they have conceded in 12 games, including their three group stage wins.
Austria, in their first-ever Euro knockout game, initially closed down the spaces well and almost took the lead when Marko Arnautovic had a second-half header chalked off for a tight offside.
