Denmark could become the first European team to qualify for the 2022 World Cup at this pace.
An impressive 4-0 win in Austria on Wednesday made it a perfect three wins for the Danes in Group F after the first week of the campaign.
Europe's top-scoring team has netted 14 goals so far — and none by playmaker Christian Eriksen — without allowing an opponent to score against goalkeeper Kasper Schmeichel.
"(Schmeichel) didn't have a single (save) here or in Israel," Denmark coach Kasper Hjulmand told broadcaster Kanal 5. "That's convincing. That's strong."
Denmark is already four points clear, routing Moldova 8-0 between solid away wins against two teams, Israel and Austria, who started last week with realistic hopes of contending. The group runner-up enters a playoff round next year.
Denmark's next opponent in Copenhagen on Sept. 1 is Scotland, which rose to second place in the standings after beating the Faeroe Islands, also by 4-0.
Austria's players began the evening holding up a long banner that read "Protect Human Rights" while their national anthem played.
They contained Denmark in the first half then were swept away by four goals in a 16-minute spell midway through the second half.
The 21-year-old forward Andreas Olsen scored twice soon after coming on as a substitute to bookend strikes by defender Joakim Maehle and midfielder Pierre-Emile Højbjerg.
Højbjerg's shot into an unguarded net got a spectacular assist from Martin Braithwaite. The Barcelona forward let the ball run on untouched while leaping to hurdle a wild sliding challenge by Austria goalkeeper Alexander Schlager far outside the penalty area.
"I don't want to point fingers. I take responsibility. Now we will focus on the Euros," said Austria coach Franco Foda. His team opens on June 13 against the lowest-ranked team at Euro 2020, North Macedonia, which won 2-1 at Germany on Wednesday.
Before the game in Vienna, Denmark's players again wore T-shirts in the "Football Supports Change" campaign by European national teams drawing attention to labour rights issues in World Cup host nation Qatar.
Scotland midfielder John McGinn scored twice against the Faeroes in Glasgow to extend his prolific run under coach Steve Clarke of 10 goals in less than two years.
Israel rose to third place in the standings by winning 4-1 in Moldova, which took the lead in the first half and had forward Ion Nicolaescu sent off when the scores were level.
