Denmark booked their spot in the Euro 2024 finals with a 2-1 win in their crunch match against Slovenia.
Albania also qualified on Friday, drawing 1-1 in Moldova to ensure they would finish in the top two in Group E.
The Czech Republic drew 1-1 in Poland to leave the second qualifying place from Group E undecided.
Italy moved to second in Group C with a 5-2 home win over North Macedonia. England, who have won the group, eased to a 2-0 home win over Malta.
In Group H, both teams were able to qualify with a win in Copenhagen and it was the hosts that claimed the spoils, courtesy of goals either side of the break by Joakim Maehle and Thomas Delaney.
Denmark had the better of the opening exchanges and were rewarded when Maehle slid in at the far post to tuck away an in-swinging cross on 26 minutes.
But the lead only lasted four minutes before Erik Janza curled a left-footed free-kick beyond Kasper Schmeichel.
A tight, tetchy affair was swung in Denmark's favour nine minutes after half-time when Delaney controlled and finished in the box after Jannik Vestergaard's flick-on.
Earlier, Kazakhstan won 3-1 at home to San Marino to move to 18 points, one behind second-placed Slovenia.
Islam Chesnokov struck in the 19th and 51st minutes but Simone Franciosi hit back on the hour for the minnows, before Abat Aimbetov's penalty in added time killed off San Marino's hopes of a rare point.
In the same group, Finland kept themselves within a win of third place by beating Northern Ireland 4-0 in Helsinki.
- Albania progress with draw -
Earlier, Albania clinched a place at Euro 2024 despite conceding a late equaliser as a they drew 1-1 in Moldova.
Sokol Cikalleshi put the visitors ahead with a first-half penalty and although Vladyslav Babohlo levelled with three minutes left, the point ensured Albania will finish in the top two in Group E.
It will be Albania's second appearance at a major tournament after their debut at Euro 2016.
Czech Republic had the chance to seal up the Group E qualification spots when they travelled to Poland but could only draw 1-1.
Jakub Piotrowski scored on 38 minutes and although the Czechs levelled through Tomas Soucek four minutes into the second half, they were unable to force a winner that would have ensured an automatic place in Germany next year.
Italy survived a scare against North Macedonia in Rome, which saw them move into second in the group ahead of Ukraine.
Matteo Darmian headed in the opener and Federico Chiesa grabbed a quick-fire brace in the first half.
Jani Atanasov pulled one back for the visitors early in the second half, before scoring a second with 16 minutes remaining but Giacomo Raspadori and Stephen El Shaarawy struck for Italy to ensure the victory.
Ukraine and Italy meet on Monday, a draw will ensure the Italians automatic qualification thanks to their better head-to-head record, following September's 2-1 win in Milan.
Am experimental and disjointed England team beat winless Malta 2-0 through an Enrico Pepe own goal with eight minutes gone and a second-half Harry Kane strike.
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