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The triumph also promoted them to the top-tier Indian Super League.
Sergio Barbosa da Silva scored both the goals for Delhi in the second half.
Mohammedan SC, who beat NEROCA 2-0 in an earlier kick-off at Shillong, lead the table with 47 points from 20 games.
The loss has almost dashed the Malabarians' title hopes.
The visitors drew 1-1 in a thrilling I-League match at Naihati on Friday.
The match ended 2-1 in favour of the Kolkata side leaving Gokulam fourth in the table.
The result set Gokulam on the right path in their quest to win a hat-trick of titles in the I-League.
The reserves of Kerala Blasters were beaten 0-3 in the quarterfinals of the prestigious tournament.
In a thrilling final round match, Gokulam Kerala edged Mohammedan Sporting 2-1 to be crowned champions.
Mohammedan are searching for their maiden title, while Gokulam Kerala are aiming to become the first team in the I-League era to defend their crown.