European champions Spain were already through to the quarter-finals but needed to win at Parken Stadium to progress as Group A4 winners.
Mikel Oyarzabal opened the scoring in the 15th minute when he latched on to Ayoze Perez’s pass before slotting in.
Former Newcastle and Leicester winger Perez got on the scoresheet himself in the second half when he finished off a flowing Spain attack, firing beyond Kasper Schmeichel and into the bottom corner.
Gustav Isaksen gave Denmark some late hope when he prodded in but they could not find an equaliser before the final whistle.
The defeat for Denmark means they still have work to do if they want to join Spain in progressing.
They are second in group but face Serbia on Monday in a fight for a finish in the top two.
