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Joakim Maehle scored five goals in the nine games he has played for Denmark.
After qualifying for the 2022 World Cup Qatar in Qatar, Denmark's captain Simon Kjaer said they could "go a long distance" with a win over Austria in Copenhagen.
Joakim Maehle's second half goal helped the Danes maintain their 100% record in GroupF.
They will also travel to Middle East after impressing at Euro 2020, where they reached the semi-finals.
Kjaer stated that although we have made great strides, we are still hungry.
We have built a team and a mentality that are incredibly healthy. We have always been eager to improve. We all share our best and that is what makes us a great team.
Maehle's goal was not more than the Danes deserve. He swept a low effort into a bottom corner after Thomas Delaney's fantastic run.
With two matches remaining, their eighth consecutive win leaves them seven points ahead of second-placed Scotland.
The result, along with Scotland's late win in Faroe Islands means Austria's chances of reaching the finals depend on last year's Nations League performance that got them into the playoffs.
