Denmark, who crushed Moldova 8-0 on Sunday, top the standings on nine points with 12 goals scored and none conceded. Scotland are second on five points, one ahead of Israel and Austria.
After a tight first half in which Joakim Maehle went closest to breaking the deadlock for the Danes, the game opened up and the introduction of Skov Olsen for Yussuf Poulsen in the 55th minute proved pivotal.
Three minutes after that switch, midfielder Thomas Delaney got free down the left and played a brilliant angled pass that left Olsen the simple task of smashing it into the net.
Maehle made it two five minutes later before Martin Braithwaite kept his cool in a race against keeper Alexander Schlager, jumping over the ball before squaring it for Pierre-Emil Hojbjerg to score Denmark's third.
Olsen rounded out the scoring with his second, latching on to a long ball and twisting inside and then out before firing a left-foot rocket past Schlager in the 74th minute.