Shane Duffy rescued a point for the Republic of Ireland with a late header in Denmark.
It was Duffy's third international goal, with his last two coming against Age Hareide's Danes.
The draw means the Boys in Green have collected seven points from their opening three Euro 2020 qualifying matches, and means Mick McCarthy has yet to taste competitive defeat in his second spell in charge.
McCarthy kept faith with the same eleven that beat Georgia last time out, with Matt Doherty once again being omitted from the starting lineup.
Darren Randolph was called into action in the 11th minute, palming a Christian Eriksen free kick wide.
Two minutes later, the Irish 'keeper got down sharply to stop Martin Braithwaite's low drive from the edge of the area.
Ireland produced some decent football in the opening stages, and had their biggest chance of the half in the 21st minute.
Conor Hourihane whipped a wicked free kick into the box, which Duffy attempted to bundle over the line, but Schmeichel managed to keep it out.
It was Denmark who took control of the half from that point, with the home side creating several dangerous openings.
However, in a common refrain when these two sides meet, the first half ended scoreless at Parken Stadium.
Ireland have now failed to score in the first half of their last nine away matches.
There was far more intensity and action after the interval.
Early in the second half, McClean caught Kjaer napping on the ball and fed McGoldrick, who pushed the ball out wide to Brady.
The Burnley winger cut inside and squeezed a pass through McClean on the left of the Denmark box.
The Derry native’s low strike was pushed behind for a corner by Schmeichel at his near post.
A minute later, Brady’s in-swinging Cross from the right flank was headed narrowly over by McGoldrick.
In the 58th minute, the lively Poulssen pounced on a loose ball and drove forward, only to see his heavily deflected strike flash just wide of Randolph’s post.
Three minutes later, Braithwaite flashed a great chance over the bar after Poulsen’s clever lay off inside the area.
Almost immediately from the restart, Duffy’s misjudged backwards header out Jorgensen through on goal, but he skied his shot under pressure from Keogh.
Alan Judge replaced Brady - who looked unhappy at the decision - in the 65th minute, with Ajax’s Kasper Dolberg coming on for Braithwaite at the same time for the hosts.
Denmark continued to squander big chances, but eventually opened the scoring in the 76th minute.
It was Hojbjerg, who replaced Lasse Schone four minutes earlier, who made the breakthrough.
The Southampton midfielder burst into the box and directed an excellent header past Randolph from Jens Stryger Larsen's cross, just beating Richard Keogh to the ball in the air.
Disaster for Ireland as Pierre-Emile Hojbjerg's glancing header beats Randolph #denirl #rtesoccerhttps://t.co/xyydabdL7Y pic.twitter.com/jAKDR7GrFP — RTÉ Soccer (@RTEsoccer) June 7, 2019
Denmark had not conceded in eight home internationals, and the visitors rarely looked capable of restoring parity from open play.
Andreas Christensen fouled substitute Judge midway inside the Danish half with five minutes remaining.
Hourihane's deliveries were impressive all night, but it was Judge who produced a fantastic delivery on this occasion.
The winger's pinpoint cross was attacked with typical vigour and aggression by Duffy, and Schmeichel was powerless to stop the towering centre half's header from flying into the net.
📺 The cross from Judge 😍 The header from Duffy 😍 🇩🇰🇮🇪 #DENIRL #COYBIGpic.twitter.com/4a2Vytonvi — FAIreland ⚽️🇮🇪 (@FAIreland) June 7, 2019
McCarthy's men held out to secure a crucial away point, and are now in an excellent position ahead of Monday's clash with Gibraltar at the Aviva Stadium.
Elsewhere in Group D, Georgia comfortably beat Gibraltar 3-0 at home.
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