Despite their dismal showing in the Danish capital, Poland remain top of the group on 16 points after seven matches, with Montenegro, who hammered Kazakhstan 3-0, second on 13, ahead of Denmark on goal difference.
The outstanding Christian Eriksen found Thomas Delaney with a corner after 15 minutes, and the midfielder picked the perfect time to net his first international goal for Denmark, forcing the ball in with a combination of his head and his right shoulder.
Andreas Cornelius doubled the advantage in the 42nd minute, volleying Eriksen's pinpoint cross into the ground and sending it bouncing over goalkeeper Lukasz Fabianski.
Poland pressed forward early in the second half but the fleet-footed Eriksen never stopped tormenting them, and on the hour mark he was at it again, rifling the ball towards goal.
Fabianski could only parry the ball into the path of Nicolai Joergensen, who slotted it in to make it 3-0.
As Poland continued to press forward, Eriksen finally got the goal he so richly deserved in the 80th minute, curling a beautiful shot past Fabianski to round off the scoring.
Denmark travel to second-from-bottom Armenia for their next game on Tuesday morning AEST, while Poland take on bottom side Kazakhstan at home.
Montenegro won 3-0 in Kazakhstan, Marko Vesovic putting the visitors ahead after 31 minutes, with Fatos Beciraj and Marko Simic on target in the second half.
Romania beat 10-man Armenia 1-0 in Bucharest with a last-minute goal form Alexandru Maxim.
Armenia had defender Taron Voskanyan sent off for handball when conceding a penalty early in the second half, but Bogdan Stancu saw his spot-kick saved by Grigor Meliksetyan - only for Maxim to have the final word with a close-range finish.
Slovakia stayed on course to qualify for their second FIFA World Cup as an independent nation after a late Adam Nemec goal gave them a crucial 1-0 home win over Slovenia in an action-packed group F qualifier.
The result left Slovakia second in the standings with 15 points from seven games, two behind leaders England who stayed in the driving seat for automatic qualification with a 4-0 victory in Malta.
Scotland moved one place up to third on 11 points after a 3-0 win in Lithuania, ahead of Slovenia on goal difference with both teams still in with a slim chance of reaching next year's tournament in Russia.
Slovenia goalkeeper Jan Oblak made six vital saves in the first half, keeping out two stinging shots apiece from Marek Hamsik and Robert Mak while he also parried a pair of close-range efforts by Nemec.
Mak shot just wide of the far post shortly after the break as the visitors continued to soak up pressure and the home side showed continued profligacy in front of goal.
Their adventurous 4-3-3 formation, akin to the one that impressed in the 2010 FIFA World Cup in South Africa when they reached the last 16, was finally rewarded in the 81st minute.
Livewire Mak broke down the right, yet again, and squared the ball into the five-yard box for Hamsik to hit the underside of the bar and Nemec bundled in the rebound for his fourth international goal in as many games.
Northern Ireland remain second in Group C after a 3-0 away win over bottom side San Marino, but are now seven points clear of the Czech Republic, whom they face at Windsor Park on Tuesday morning AEST where a draw would secure runners-up spot.
Michael O'Neill's men, though, left it late, having been frustrated for 70 minutes by a team that have never won a competitive fixture.
Josh Magennis's five-minute double and Steven Davis's penalty all arrived in quick succession to eventually get the job done and seal a record fourth successive victory.
Elsewhere in Group C, Norway beat Azerbaijan 2-0 in Oslo with a first-half penalty from Bournemouth forward Josh King and an own goal after 66 minutes from Rashad Sadygov.
Azerbaijan finished the match with 10 men after midfielder Javid Huseynov was sent off in the final minute for a second caution.
The nine group winners in Europe will qualify automatically for the 32-team event, while the eight best runners-up enter a two-leg play-off for an additional four berths.