RB Leipzig forward Poulsen unleashed a spectacular strike into the top corner in the 71st minute before Tottenham midfielder Eriksen scored a second moments later.
Denmark edged most of the game, and aside from a couple great saves from Guillermo Ochoa, the scrappy first half was almost entirely forgettable.
Chances were extremely limited for El Tri, and after a flurry of substitutions at halftime, they struggled to find any sort of rhythm.
Denmark, on the other hand, began the second period with more purpose, although little was being created by either side.
The deadlock was eventually broken in the 71st minute when Yussuf Poulsen found himself with space at the edge of the box to cut inside and score a superb goal.
The visitors were then made to pay moments later following some terrible defending at the back. After a throw-in, Christian Eriksen sealed the home side’s success, firing through Guillermo Ochoa for the 2-0.
Javier “Chicharito” Hernandez had a golden opportunity to get a goal back when he struck the post, but El Tri eventually succumbed to defeat in Copenhagen.