Dempo scored through Sushil Kumar Singh (26th min) and substitute Tolgay Ozbey (82nd, 90+3) who was latter awarded the man of the match.
While Royal Wahingdoh reduced the margin through Loveday Okechukwu (45+1) and Densil Theobald (85th).
The win takes Dempo to 16 points from 14 matches while Royal Wahingdoh remained on 26 points from 16 games.
Royal Wahingdoh are fighting for the title and the home team is fighting to avoid relegation. Dempo looked the better side in the first half as they had more of the ball possession and had an early chance to take lead in the 16th minute but Jewel Raja missed an easy sitter.
The visitors who came close on couple of occasions nearly equalised in the 41st minute when a snap shot from Denzil Theobald was put out by keeper Katimani.
It looked Dempo would go into the break with a 1-0 lead but lack of concentration by their defender in injury time saw them concede a goal.