The first 45 minutes were played at an electrifying pace with plenty of aggression from both sides but despite a number of chances at both ends, neither could find a way to break the deadlock.
Copenhagen keeper Robin Olsen made a scrambling double save to thwart Andre Silva midway through the second half and he was called into action on several other occasions as the Danes hung on to keep their hopes of qualifying for the knockout stage alive.
English champions Leicester City top Group G on 13 points after handing bottom side Club Bruges their fifth straight defeat in the competition, with Porto in second on eight points and Copenhagen third on six.
Porto, who would have qualified for the last 16 with a win in Copenhagen, now host Leicester in their final group game on December 7, while the Danish side travel to Club Bruges.
(Reporting by Philip O'Connor in Stockholm, editing by Simon Cambers)
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