The result will nearly certainly see the end of manager Gianpiero Ventura, while the loss marks the end of superstar goalkeeper Gianluigi Buffon's time in the national team.
It was a far more industrious effort from the four-time world champion at San Siro than the drab effort produced in the first leg, and visiting goalkeeper Robin Olsen was at his best to keep Italy at bay at the end of a busy first half.
Italy's streak of 14 consecutive World Cup appearances is snapped.
At 39, the 175-times capped Buffon had announced that the finals in Russian Federation would be his last as a player for the national side. The last time the Scandinavians participated was in 2006.More news: Roy Moore Being Persecuted Like Jesus, Says Brother After Child Abuse Allegation
The closest the hosts came to scoring was a Ciro Immobile effort, which was partially stopped by Olsen and cleared away by Victor Lindelof as it was about to trickle over the line.
Mikael Lustig nearly scored an own goal when his deflection hit the bar.
Gian Piero Ventura will surely need to make some modifications to his lineup after such a poor performance in Stockholm. Napoli's in-form winger Lorenzo Insigne however was once again left on the bench.
Sweden were dealt a blow in the 17th minute when Johansson was injured while lunging for the ball and had to be stretchered off the pitch.More news: Sean Hannity fans boycott Keurig, but will it make a dent?
Jorginho's through ball found Immobile to pull back from the byline for Candreva to blast over, but Leonardo Bonucci, wearing a protective mask after breaking his nose on Friday, got a knock to the knee and was limping badly.
"We must be confident in the return leg, otherwise we have already lost".
With three minutes remaining, Italy poured bodies forward and Stephan El Shaarawy's expert volley drew a fine stop from Olsen, and Parolo nodded wide from an inviting position shortly after.More news: Takeaways from Lions' 38-24 win over the Browns
Italy, who have won the World Cup on four occasions, the last time in 2006, will be the most high profile absentee from the finals in Russian Federation next year.