The Danes have won all six of their games, scoring 22 goals while conceding none, and top the standings with 18 points. They now boast a seven-point lead over second-place Scotland, with Israel a point further back and four games left to play.
Damsgaard, the 21-year-old Sampdoria midfielder who broke into the national team side after Christian Eriksen suffered a cardiac arrest in their opening Euro 2020 match in June, was once again the creative fulcrum, and it was his shot that was parried into the path of Yussuf Poulsen, who scored the opener in the 28th minute.
Captain Simon Kjaer added a second three minutes later and Andreas Skov Olsen also netted before the break. Thomas Delaney then scored in the 58th minute before Andreas Cornelius added a fifth in stoppage time to complete a dominate Danish performance in Copenhagen.