Chelsea midfielder Jorginho's 79th-minute penalty in Tampere made it six wins from six for Roberto Mancini's side.
Tampere: Jorginho fired Italy to within touching distance of Euro 2020 with a spot-kick winner that beat nearest rivals Finland 2-1 on Sunday and maintained his side's perfect qualifying record.
Chelsea midfielder Jorginho's 79th-minute penalty in Tampere made it six wins from six for Roberto Mancini's side and sent them six points clear of the second-placed Finns in Group J, after in-form Norwich City striker Teemu Pukki had levelled Ciro Immobile's headed opener with a penalty of his own six minutes before.
With two teams qualifying from the group, four-time world champions Italy are flying high with a maximum 18 points with four qualifying games to play, nine points ahead of third-placed Armenia despite their thrilling 4-2 win over Bosnia and Herzegovina earlier on Sunday.
They could now secure qualification for the tournament, which kicks off in Rome next June, against Greece or Liechtenstein -- who surprisingly drew in Athens -- next month.
"The match against Greece could be the one that secures qualification and we hope the Stadio Olimpico will be as full as during the 1990 World Cup when we were young," said Italy coach Roberto Mancini.
Former Italy international Mancini took over last year after the Azzurri's failure to qualify for the 2018 World Cup.
"There was a bit of suffering, but we dominated the game," he added.
"The lads did very well overall, although we had a few scares when it was 1-1.
"But there were so many things that I liked, dominating away from home every time is very positive and even the substitutes did very well, having more players to choose I think is fundamental.
"Our nature is to always attack, you could see that tonight, giving very little to our rivals."
Finland -- bidding to qualify for the European Championship for the first time -- have lost both their matches to the Italians after also falling 2-0 in Udine last March.
'Feeling the pressure'
The Italians had the best of the first half, dominating possession against the Finns who have won four matches out of six.
Finland goalkeeper Lukas Hradecky did well to deny a Stefano Sensi volley with Immobile getting his head to a Federico Chiesa cross but sending it wide.
Sensi again missed a chance to give Italy the advantage just before the break with Hradecky blocking a Chiesa effort.
Pukki threatened after the break but Italy's pressure paid off in the 59th minute, with Chiesa racing down the right to set up Immobile who nodded in his first international goal in two years.
"I was feeling the pressure of not scoring with this jersey," said Lazio striker Immobile whose last international goal was in a World Cup qualifier against Israel in September 2017.
"But I knew the time would come. Tonight wasn't easy, but we did well. We are happy, we are starting again after the disappointment of missing out on the World Cup."
Italy looked to have thrown away the win when Sensi tripped dangerman Pukki in the box, with the striker easily beating Gianluigi Donnarumma from the spot to score his fifth of the qualifying campaign.
However seven minutes later Italy were ahead again, with another penalty taken by Jorginho, after being fouled by Robin Lod.
The Brazil-born midfielder netted the winner to ensure all three points with just his second Italy goal, one that has all but booked his team's place at the Euros. Italy next play Greece on October 12 in Rome.