Sorabuddin Mollick (12th), Jatin Bisht (58th) and Eric Brown (90+4) scored for the winners while Peter Carvalho struck the consolation goal for Dempo.
ONGC showed intent from the beginning, proof of which was the early strike, which, at the same time, also highlighted Dempo goalkeeper Subhasish Roy Chowdhury's poor work at the post.
Mollick put the well-organised hosts ahead when he scored off a rebound after Kailash Patil's attempt off Brown pass found Chowdhury.
Dempo fluffed a few chances in the period post the early goal, and there were also a couple of opportunities for the home side.
Dempo's hopes of a fightback went up in smoke after Bisht fired in a rasping volley from just outside the box, his class act giving OGNC a 2-0 lead moments from the start of second half.
After a none-too-impressive outing in the midfield, Carvalho brought the margin down and gave Dempo a glimmer of hope when he tapped in Clifford Miranda's free-kick at the Ambedkar Stadium.
The match was sealed beyond issue when Brown found the net seconds before the final whistle, to give his side its first win of the league.
The key to ONGC's success was the domination in the midfield. Dempo prefer to play a free-flowing game but ONGC's tight marking meant none of the Dempo players got enough space in the middle.
Man-of-the-Match Robin Gurung also deserves special mention for without his strong presence at the back, ONGC could have found it difficult.
Dempo's Japanese Ryuji Seoka showed spirit but not opportunism, and he also lacked a dangerous striking partner. (More)
