Denmark dominated the first leg of the play-off and started confidently at the Aviva Stadium on Tuesday night, with Darren Randolph making a brilliant early save to his right.
It was Shane Duffy, though, who broke the deadlock as the Brighton man took advantage of some poor Denmark defending to find the net with his head from close-range in the sixth minute.
Age Hareide’s men piled on the pressure after Ireland’s opener and Tottenham midfielder Eriksen began to have more of an influence as the game wore on.
The away side drew level in the 29th minute as Cyrus Christie bundled the ball into his own net and the night was about to get much worse for Martin O’Neill’s team.
Eriksen finished off a rapid counter-attack in the 32nd minute with a superb first-time shot to put Denmark 2-1 in front, meaning the Irish needed two more goals as the referee blew for half-time.
The Spurs star doubled his personal tally in the 63rd minute as he found acres of space on the edge of the box before curling the ball beyond a hapless Randolph.
Eriksen became a national hero in the 73rd minute when he scored his hat-trick after capitalising on Ireland’s poor defending and drove the ball into the roof of the net to put Denmark out of sight.
Substitute Nicklas Bendtner put the icing on the cake for Denmark at the death, scoring from the spot to pile yet more misery on the home team.