This summer's European Championship Semi-Finalists had won their first seven games in Group F, without conceding, and knew that one more victory from their remaining three matches would see them join the hosts, and Germany, as the confirmed participants for next winter's World Cup.
Kasper Hjulmand's side didn't disappoint the packed crowd at Parken, Joakim Mæhle netting the only goal of the game eight minutes after the break to confirm passage through.
Christian and Mathias were both introduced in injury-time as The Danes qualified for consecutive World Cups for the first time since 2002.
For Christian it was his 14th international appearance while Mathias has 15 caps to his name, all of which have come as Brentford players.
Denmark finish qualifying with games against Faroe Islands and Scotland next month as they look to make it a perfect campaign.
In Asian World Cup Qualifying, Saman Ghoddos and Iran remain in pole position following their 1-1 draw at home to South Korea on Tuesday. Team Melli had won their opening three matches but fell behind in Tehran to Son Heung-Min's 48th minute goal. However, Alireza Jahanbakhsh levelled late on to preserve Iran's two-point lead over Korea at the top of Group A.
More importantly, with the top two automatically qualifying, Iran have a five-point cushion to third placed Lebanon who they face next month.
Saman was an unused substitute as he remains on 28 appearances for his nation.