Although Chennaiyin continue to be fourth on the ISL table with 24 points from 14 matches, the draw means they now face a tough battle to secure a spot in the semi-finals.
Fifteen minutes into the game, Delhi Dynamos had a wonderful opportunity to take the lead.
After passing the ball patiently in the midfield, Chhangte put in a tantalising ball into the box for Kalu Uche, but the Nigerian couldn't get his head to it.
A similar pattern of play continued for much of the first half.
But just before the half-time whistle, Chennaiyin could have taken the lead had Gregory Nelson shown some composure in front of goal.
Delhi looked set to take all three points from the game but with just 10 minutes left on the clock, Chennaiyin found a leveller.
Rene Mihelic's lobbed free kick was met by Alves, who rose above everyone in the box to put the ball past Irureta.
With little time left on the clock, both sides tried to find a winner but there was nothing to separate the two on the night.
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