Joakim Maehle scored in the 53rd minute to send the Danes to Qatar as they build on their surprise run at Euro 2020 this summer when they reached the semi-finals.
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.
Photos in the British press showed the green light of a laser being pointed at Kasper Schmeichel's face just before Harry Kane's extra-time penalty.
The incentive comes as the vaccine roll-out is now targeting those aged 18 and over, and England are in the last four and on the verge of their first major championship final -- and trophy -- since 1966.
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.
Already assured of playing in the last 16, England made certain that the knockout tie will be played in front of their own fans at Wembley thanks to Raheem Sterling's first-half winner against the Czechs.
Raheem Sterling scored at a sun-baked Wembley as England won their opening game of a European Championship finals for the first time at the 10th attempt.
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.
Southgate's side launch their campaign against Croatia at Wembley on Sunday, with the manager aiming to build on their run to the World Cup semi-finals in 2018. All three of England's group matches are at home and Wembley is hosting some of the knockout matches at the delayed tournament, including both semi-finals and the final.
The 23-year-old Brighton central defender made his international debut in the 1-0 friendly win over Austria last week and backed that up in Sunday's match against the Romanians.
Liverpool right-back Alexander-Arnold limped off late in the second half after injuring himself while clearing the ball.
England manager Gareth Southgate selected a provisional 33-man squad on Tuesday that included uncapped defenders Ben Godfrey and Ben White.
Postponed last year because of the pandemic, Euro 2020 finally kicks off in a month's time when Italy face Turkey in Rome but the health crisis continues to cast a shadow over a tournament being held for the first time at venues all across the continent.
Napoli midfielder Eljif Elmas secured a famous victory for North Macedonia in Duisburg, scoring five minutes from time to give his country a second win from three Group J matches.
Elsewhere, England, Italy and Germany all had to work hard in the Balkans to gain their second victories in two matches.
