The visitors arrived in Glasgow with nine wins from nine in Group F but goals from John Souttar and Che Adams earned a 2-0 win for Steve Clarke's side and wrecked Danish hopes of completing an unbeaten qualification campaign.
It was a reverse of the scoreline in Copenhagen in September when Scotland conceded two goals inside the opening 15 minutes in a 2-0 defeat that appeared to damage hopes of reaching Qatar 2022.
However, the side recovered to post six successive victories to secure a runners-up finish behind the Danes and secure status as top seeds for the World Cup play-offs in March.
Hjulmand – who led Denmark to the semi-finals of Euro 2020 – heaped praise on Clarke and his players for their transformation and hopes they can join his side at next year's tournament in the Middle East.
"We said before we met Scotland tonight that we've seen a progression," he said. "Also from the Euros until now. I think they have done a quality job.
"I think obviously they also have momentum with the people. I think the Israel game, the last minute goal, the stadium, the crowd, the atmosphere, I think it's a little bit like we see in Copenhagen. That helps a team like this.
"I think they were highly-motivated today. They played a very good match and I think Scottish football is up for something great in 2022. I definitely hope that they will join us [at the World Cup]."