England were reduced to 10 men shortly in the 31st minute when Harry Maguire picked up his second booking.
Eriksen scored from the spot after Kyle Walker had conceded a soft penalty shortly after Maguire's red car.
Mason Mount almost levelled after the break but Kasper Schmeichel pulled off a wonder save to deny him.
England threatened late on with Conor Coady having his header cleared off the line but Denmark held on.
Defender Reece James received a straight red for an incident after the final whistle at Wembley.
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