Brazilian Anderson Sebastio Cardoso's goal from the spot in the 8th minute turned out to be the matchwinner as Delhi took full three points in their second match after losing to FC Goa in their campaign opener.
Chennaiyin, on the other hand, slumped to their second consecutive defeat after losing 2-3 to defending champions Atletico de Kolkata in their previous match.
The Marco Materazzi-coached visiting side lacked sting in the attack with Steven Mendoza and Balwant Singh failing to combine together.
Jeje Lalpekhlua, who started against ATK, had to miss today's match as he is doing his national duty, while Fikru Teferra was not 100 per cent fit and came only for the last 10 minutes of the match.
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With Brazilian Gustavo Dos Santos and former France and Chelsea star Florent Malouda making an impact in the match, Delhi did not feel the absence of India striker Robin Singh -- away in Turkeministan in national colours -- and they had more chances in the match though Chennaiyin were the better side in the second half.
The referee promptly pointed to the dreaded spot and Cardoso cooly placed the ball past a diving Chennaiyin goalkeeper Apoula Edel Bete to the wild celebration of the 19,453 home team supporters.
Chennaiyin goal came under threat once againt in the 21st minute with Santos, after a one-on-one with Florent Malouda, cut into the left side of the visiting team. But, the Brazilian, instead of passing the ball to Richard Gadze, attempted a shot from an acute angle at the near post which was collected by the goalkeeper.