The deadlock was broken in the 95th minute when substitute Federico Chiesa struck a beautiful left-footed strike into the bottom left corner before substitute Matteo Pessina found the other corner in the 105th minute to stretch the Azzurri's lead.
A deft header from Austria's Sasa Kalajdzic halved the deficit but it was not enough as the Italians remained confident and composed as it continues to impress.
The victory on Saturday at Wembley Stadium in London also means Italy has now won its last 12 consecutive matches.
It was also Italy's 31st game in a row without defeat, surpassing the record of 30 set by the team between 1935 and 1939 under Vittorio Pozzo.
Italy now advances to the quarterfinal where it will face the winner of No. 1 ranked Belgium or reigning champions Portugal.
Either side will be the biggest challenge the Italians will have faced so far in this tournament, with the last time it lost a match coming against Portugal back in September 2018.
"Austria played well but we had our chances and we scored a couple of good goals," Chiesa said afterwards. "I think we deserve to go through. We are a group of 26 players and all of us are eager to help the team win games. This is what made the difference tonight."
Like in Rome
Despite the reduced crowd capacity at Wembley, the roar of the Azzurri fans when the players emerged and the passionate signing of the national anthem was like the team was playing in Rome.
Due to current guidelines, arrivals from Italy are not able to travel to the United Kingdom without undergoing a mandatory quarantine period.
But despite the match taking place in London, Roberto Mancini's side surely would have felt as though it were playing in front of a home crowd.
Austria was playing in its first ever knockout match at the European Championships in its third appearance at the tournament.
It was also the first major tournament in which Austria have progressed beyond the initial group stage since the 1982 FIFA World Cup in Spain.
Lack of experience at this stage did not show during the first 90 minutes as Austria executed a decisive tactical plan, defending well and taking its opportunities on the counterattack.
Striker Ciro Immobile came closest for Italy in the first half though, hitting the post from outside the area with a thunderous strike.
Austria nearly grabbed an unlikely win in the 65th minute, but Marko Arnautovic's header was ruled out by the video assistant referee for offside.
However, in extra time, the speed and intensity of the Italians was too much for Austria to contain.
Austrian goalkeeper Daniel Bachmann did all he could to keep his team within striking distance of the quarterfinals but was left helpless with the two near-perfect strikes from the Italians.
It was two substitutes who did the damage for Italy with Chiesa's left footed strike breaking the deadlock late on, before Pessina extended the lead with his own left foot.
Pessina was a late addition to Italy's squad following the withdrawal of injured Stefano Sensi and has now scored two goals in two games at the tournament.
Kalajdzic's late header proved a mere consolation for the Austrians but was the first goal the Italians had conceded at Euro 2020.
In the end it was heartbreak for Austria who performed above expectations and will return home with its head held high.
"You saw over 120 minutes that it was a very mature performance," Austria head coach Franco Foda said afterwards.
"Now it's about backing that up when we return in September. You saw that the team was hungry and had a good spirit and a good plan. From September, we need to prepare ourselves as best as possible because we want to go to the [FIFA] World Cup in Qatar."
Italy continue to prove to its opponents why it is a contender to win the tournament and lift its first European crown since 1968.