With Montenegro winning 3-0 at Kazakhstan, Poland's lead was trimmed to three points with three games remaining.
Montenegro and Denmark are tied on points behind the Poles.
Denmark playmaker Christian Eriksen set up goals for Thomas Delaney and Andreas Cornelius in the first half, before scoring himself in the 80th to wrap up a surprisingly one- sided match at Telia Parken in Copenhagen. Nicolai Jorgensen scored the third goal, in the 59th minute.
Marko Vesovic, Fatos Beciraj and Marko Simic were the scorers for Montenegro in Astana.
Romania beat Armenia 1-0 thanks to midfielder Alexandru Maxim's goal in the first minute of stoppage time. Romania is fourth in the group, four points behind Montenegro and Denmark.