Andre Signoretti skated through two Latvian defenders and fed Cirone, who took the pass off his skate and then sent the puck past the outstretched pad of Latvian goaltender Sergejs Naumovs at 4:10 of the five-minute overtime period.
"It was a pretty easy goal for me," Cirone said. "Andre did all the work taking three guys with him and all I had to do was shoot it in."
In Mytischi, Michael Wolf scored twice to lead Germany to a 5-3 victory over Norway and a place in the qualifying round.
Italy, which improved to 1-2 in the preliminary round, finished third in Group A and will face host Russia on Friday in the qualification round.
Italy looked set for the win in regulation but Lauris Darzins scored his second goal of the game, taking a pass from Mikelis Redlihs and beating Italy goalie Guenther Hell at 18:09 to tie the game at 3-3 and force overtime.
Latvia scored midway through the third to go up 2-1 on a goal by Kaspers Daugavins but Italy tied it at 16:41 when Luca Ansoldi's shot deflected off a Latvia defender and got past Naumovs.
Italy then took a 3-2 lead one minute later when Naumovs gave up a huge rebound and Christian Borgatello sent the puck in from the faceoff circle.
Italy tied the game 1-1 early in the second period when Cirone tapped in a rebound through the legs of Naumovs at 3:03.
Latvia scored the only goal in the first period. Darzins redirected a shot from the point and then picked up his own rebound before sliding the puck past Hell at 14:57.
Latvia will play in the relegation round along with Norway, Ukraine and Austria.
Germany jumped out to a 2-0 lead on power-play goals from Michael Hackert and Wolf in the opening period.
But after the break, Norway pulled ahead with three quick goals by Mats Trygg, Morten Ask and Lars Erik Spets.
Their lead was short-lived, however, as the Germans immediately responded with a scoring spree of their own. Wolf scored his second just 25 seconds later, with John Tripp adding what would be the game winner less than three minutes after that.
Alexander Barta added the insurance goal at 22:51.
"We played desperate hockey today," Germany coach Uwe Krupp said. "Both teams were very evenly matched. Tomorrow we have a very difficult opponent in the Czechs, who had the day off today. They are the strong team with more talent and more experience. But we'll fight."