An own goal from Souvik Chakraborty (3rd minute) opened the scoring for the hosts before Reinaldo Da Cruz Oliveira (45'+2') added a second at the stroke of half-time.
The visitors, who had better ball possession and scoring opportunities, failed to find the net with rival goalkeeper making a couple of good saves.
After being gifted with an early lead, the Zico coached side continued to make the right moves even though the ground was a bit slippery post some drizzle before the match.
Delhi, who lost both their matches to the home team last season, seemed unperturbed by the early setback and regrouped to create chances. They had a chance to find the equaliser but the hometeam keeper Elinton Andrade did well to come out of his charge and deny Richard Gadze from scoring from a one-to-one situation.
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The visitors kept on probing and had another chance to find the equaliser but Florent Malouda header off Vinicius Ferreira de Souza cross from the left went over the bar.
The Goan team, who played a waiting game, scored again in the injury time of the first half. Joffre Mateu Gonzalez, who was brought down just outside the box by defender Vinicius, took the free kick and sent a goal mouth shot, which Reinaldo Oliveira deflected it into the net to have the home team leading 2-0 at half time.
Malouda was once unlucky when his kick hit the post.
Delhi defense, moving upfront in search of a goal, nearly conceded another goal as the home team came with a counter move towards the end.