Red Bull Leipzig forward Yussuf Poulsen scored the only goal of the game as Kasper Schmeichel shone for a resilient Denmark side in Saransk.
Poulsen was earlier penalised via VAR for a challenge inside the area, for which the referee awarded a penalty. Christian Cueva stepped up, but he fluffed his lines from 12 yards.
From villain to hero Poulsen turned his fortunes around minutes later, as he broke the offside trap and slotted home a composed finish with his left foot.
It was Schmeichel who saved Denmark on a number of occasions however, as he made a catalogue of saves as the minutes ticked on toward full-time.
Denmark now sit second on goal difference at the top of Group C, behind France.