Italy only needed the draw in a game played in Leverkusen, Germany, in order to qualify but a defeat against their direct rivals in Group C would have left their fate to be decided in play-offs next March.
Bruno Fernandes and Ricardo Horta netted the goals for Roberto Martinez's Portugal, with Cristiano Ronaldo not on the scoresheet, to end with 10 wins from 10 matches in Group J.
Les Bleus set a new record margin of victory in European qualifying and a national record in Nice.
Albania also qualified on Friday, drawing 1-1 in Moldova to ensure they would finish in the top two in Group E.
Needing a point to be certain of qualifying for next year's tournament in Germany, Gareth Southgate's side fell behind to Gianluca Scamacca's early goal.
France international Jean-Clair Todibo on Monday apologised for laughing during a minute's silence in memory of the victims of the Israel-Hamas conflict and a murdered French teacher before a Euro 2024 qualifier last week.
Ronaldo netted his 126th and 127th Portugal goals, further extending his record as the top all-time men's international goalscorer.
Spectators at the King Baudouin stadium in the Belgian capital were told to remain inside the ground following an announcement that the players would not return for the second half
Barcelona midfielder Gavi scored the only goal early in the second half in Oslo, bouncing a shot into the corner to help Spain qualify for next year's finals in Germany with two games to spare.
Giacomo Bonaventura curled in his first Italy goal and Domenico Berardi produced a fine strike of his own to double the lead in Bari.
Portugal coach Roberto Martinez hailed superstar Cristiano Ronaldo following his match-winning performance against Slovakia in the Euro 2024 qualifiers on Friday, mentioning the 38-year-old as a 'reference point for young players'.
France, Belgium and Portugal all blinked with a Euro 2024 place in their grasps but clung on for one-goal victories on Friday night which made them the first sides to qualify for next year's tournament.
AS Roma forward Stephan El Shaarawy was called up to the Italy team on Friday after Sandro Tonali and Nicolo Zaniolo were sent home amid a probe into alleged gambling offences.
Elsewhere, Turkey, in their first game under Vincenzo Montella, won in Croatia to vault to the top of Group D and Albania tightened their grip on Group E with a comfortable win over the Czech Republic.
Ferran Torres scored twice to help Spain earn a comfortable 6-0 win against bottom side Cyprus in a Euro 2024 Group A qualifier on Tuesday, with Barcelona prodigy Lamine Yamal becoming his country's youngest-ever starter aged 16 years and 61 days.
Roberto Martinez's side have now won all six of their qualifying games, without conceding a single goal and scoring 24 themselves, with this the country's largest ever victory.
England lead the group on 13 points with Ukraine on seven. Italy and North Macedonia both have four points.
Lamine Yamal brightened the gloom that has descended over Spanish football by becoming the country's youngest ever player and goalscorer as La Roja thrashed Georgia 7-1 on Friday to get their Euro 2024 qualifying campaign back on track.
The win lifts the Norwegians to third in the five-team group on four points from four matches, behind second-placed Georgia on goal difference while Scotland, who are hosting Georgia on Tuesday, top the group with nine points from three games