The Blues started brightly and almost broke the deadlock in the fourth minute when Jores Okore's desperate defensive header rebounded off his own post.
Okore had been put under severe pressure by Victor Moses, who was making his debut in European club football.
The breakthrough came 12 minutes before half-time. Fernando Torres found Frank Lampard on the edge of the area and the England midfielder slipped in Juan Mata, who beat goalkeeper Jesper Hansen with a low first-time effort from nine yards.
Torres and Moses both had goals correctly ruled out for the visitors. The Spaniard was denied by the offside flag on the stroke of half-time, before Moses saw his second-half effort ruled out for a push on Michael Parkhurst.
Nordsjaelland, who were competing in their first ever Champions League fixture on home soil, breached the Chelsea backline on a couple of occasions.
Mata decisively ended a scrappy piece of play with a driven finish from 10 yards on 82 minutes.
Ramieres then completed the rout from close range in the dying seconds.
Prior to today, Chelsea had only won once in their previous seven continental matches away from Stamford Bridge.