After Ryuji Sueoka (12th minute) and Climax Lawerence (first half injury time) put Dempo ahead, Chhetri scored twice to help Churchill Brothers draw the match and split points.
Churchill Brothers' tally now stands at 48 points from 23 matches. Dempo, who are on fifth place, took their tally to 36 points from 24 matches.
Both sides played an attacking game in the first half where Churchill Brothers had more of the ball possession. But Dempo keeper Subhasish Roy Chowdhury was alert under the bar and denied Churchill Brothers an early lead.
Minutes later Sueoka would have scored again but timely intervention by rival keeper foiled his attempt.
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Churchill created a couple of scoring chances but first Henri's attempt at the goal went out and later Chhetri's try was saved by keeper Chowdhury.
Churchill earned a free kick just on top of the box after defender Sameer brought down Chhetri. Chhetri took the free kick and found the far corner of the net to restore parity in the 43rd minute.
Chhetri, who is good in dead ball situation, once again brought Churchill in level term after the change of ends when he beat keeper Chowdhury all ends to find the far corner of the net from a free-kick in the 53rd minute.
The match became more exciting after the goal as both teams went all out in search of the winner. However, neither of them succeeded and the match ended in a draw.