Inspired by the peerless Messi, Argentina raced into a two-goal lead in the first half of the prestigious friendly thanks to strikes from Lautaro Martinez and Angel Di Maria.
The Italians needed to match Switzerland's result to qualify directly but while Roberto Mancini's side could only stutter to a stalemate, the Swiss went on the rampage in Lucerne to book their ticket for Qatar.
Ferran Torres struck twice in the first half to make sure that Luis Enrique's Spain won the Final Four clash at the San Siro in Milan, where they will face either France or Belgium in Sunday's final.
Roberto Mancini's Italy are on a world-record run of 37 matches without defeat and have a squad predictably stuffed full of players who took part in their run to glory in the Euro final over England at Wembley.
Elsewhere, Belgium thrashed Estonia, England thumped Hungary in a match marred by reported racist chanting and Germany claimed an underwhelming win against Liechtenstein in Hansi Flick's first match as coach.
Roberto Mancini's team cannot afford to rest on their laurels because until they have secured qualification for the finals in Qatar, they will not have completely erased the memory of their failure to qualify for the 2018 World Cup.
Giorgio Chiellini, the team's 36-year-old captain, and coach Roberto Mancini lifted the gleaming trophy aloft after the team's plane touched down in Rome just hours after the victory in London on Sunday night.
Three years on from their defeat by Croatia in the World Cup semi-final, Gareth Southgate's men overcame Denmark 2-1 in extra time at a rocking Wembley on Wednesday to reach their first European Championship final.
While Italy - whose only European Championship title came in 1968 - have been the standout team at the tournament so far, Spain have overcome a difficult start to reach the last four as they target a record fourth continental crown.
The Azzurri, now unbeaten in 29 matches and having won their last 10 games without conceding a goal, sit first in Group A and are guaranteed a top-two finish and last-16 berth.
France's fearsome forward line makes them favourites to win a third European crown at the pan-continental event, while top-ranked Belgium and a youthful England side will be major threats.
Italy secured first place in Group 1 with a 2-0 triumph in Sarajevo thanks to a goal in each half from Torino's Andrea Belotti and Domenico Berardi of Sassuolo.
Belgium were just five minutes from joining world champions France at next October's finals when Iceland pulled level at 1-1 with group rivals Denmark in Copenhagen.
Italy move top of League A, Group 1 while Poland registered their first points after a 2-1 win over Bosnia in Zeneca despite the continued absence of rested striker Robert Lewandowski.
Ireland needed to beat Denmark in Dublin to clinch qualification for next year's 24-team European Championship finals, but Matt Doherty's late header was only enough to earn Mick McCarthy's men a 1-1 draw at the Aviva Stadium.
Cristiano Ronaldo, 33, had been left out of the squad at his own request to focus on his new Italian club Juventus.
The four-times world champions were held to a 0-0 draw at home by Sweden in the second leg of their European playoff on Monday, losing 1-0 on aggregate, and will miss the finals for the first time since 1958.
