Both sides started the contest nervously but De Jong sparked the game into life in the 22nd minute, heading home after finding himself in space from a corner.
Frankfurt responded to the setback well but failed to pull a goal back before the half-time break.
The hosts should have been level shortly after the interval when Takashi Inui burst clear of the visiting defence. However, the Japan international fired his shot over the crossbar.
Monchengladbach defended valiantly in the final stages of the match, surviving long periods of sustained Frankfurt pressure to claim the three points.