The Danish nightmare in Copenhagen started after 27 seconds, Movsisyan firing home following a mistake by defender Simon Kjaer.
Kjaer was again the villain as Armenia doubled their lead in the 19th minute, keeping the Armenians onside as Aras Ozbiliz fired home.
Spartak Moscow striker Movsisyan netted his second on the hour mark and the Danes looked down and out, failing to create and looking vulnerable on the break as their normally slick passing touch deserted them.
With the Danes pouring aimlessly forward in search of a goal, Armenia's Henrikh Mkhitaryan added a late fourth - his goal ironically applauded by the Danish fans.
The heavy home defeat leaves Denmark in fifth place on six points, level with Armenia in fourth.
Italy lead the group on 14 points, with Bulgaria in the playoff spot in second on 10 points and the Czech Republic a point further back in third after six of 10 matches.
Two goals from captain Zlatan Ibrahimovic helped stuttering Sweden to an unconvincing 2-0 win over the Faroe Islands in their Group C World Cup qualifier in Stockholm on Tuesday.
Sweden had no shortage of possession but struggled to penetrate the massed ranks of the Faroese defence, with the home side taking over 20 minutes to register an effort on target.
Ibrahimovic broke the deadlock in the 35th minute, first playing Mikael Lustig free on the right before meeting the full back's deflected cross with a thumping left-foot volley from close range.
The hosts continued to waste their chances until the Sweden captain then struck his 41st international goal from the penalty spot in the 82nd minute after he was bundled over in the box.
The result leaves Sweden in third place on 11 points, behind Austria and ahead of Ireland on goal difference.
Germany lead the group with 16 points from their six games.
Dmitry Verkhovtsov's late header earned Belarus a 1-1 draw against Finland in their World Cup Group I qualifier in Gomel.
Verkhovtsov's 85th minute header cancelled out Teemu Pukki's first-half strike for the visitors.
- Sports & Recreation
- Zlatan Ibrahimovic
- Henrikh Mkhitaryan