Michael Krohn-Delhi cancelled out a Lukas Podolski strike to make it Germany 1-1 Denmark at the interval.
As things stand, Germany would advance to the quarter-finals along with Portugal, who are drawing 1-1 with the Netherlands.
Germany began the half in the ascendancy with Thomas Muller firing high and wide after just two minutes.
Chance after chance followed for Joachim Loew's side as Sami Khedira posed questions of the Danish defence, supplying chances for Muller and Euro 2012 joint top-scorer Mario Gomez.
Nicklas Bendtner had a half chance early on but Manuel Neuer had no trouble collecting the ball.
Germany eventually broke the deadlock on 19 minutes when Podolski thundered in a strike from the edge of the area to mark his 100th cap.
Krohn-Delhi equalised just six minutes later after heading home from close range.
Germany regrouped and once again asserted their authority as the half wore on but they could not find a second goal as they go in level at half time with everything to play for.
