Willis Plaza scored the winner for Delhi FC.
Blasters, who have three points from two matches, take on Delhi FC in their final group game on September 21.
Uruguayan midfielder Adrian Luna scored the winner off a penalty in the 70th minute.
The 25-year-old, who has joined from Punjab FC, is the fifth foreign signing made this season by the Blasters.
The Indian Super League side drew 1-1 against 10-man Bashundhara Kings of Bangladesh to reach the next round.
With just one point from two matches, the Sunil Chhetri-led team has been knocked out from the competition.
The versatile player who can play both in defence and in midfield has signed a deal till 2023.
The Indian captain is set to miss the international friendly against Oman on March 25 in Dubai.
With this, Mumbai City remained on second spot with 34 points from 17 matches while Bengaluru FC jumped to sixth with 22 points from 18 matches.
In a first for ATK Mohun Bagan this season, two first-half goals signalled the downfall for a beleaguered Bengaluru FC, who were punished for their defensive mistakes.