India striker Jeje Lalpeklhua put the defending champions ahead in the 28th minute while Anibal Rodriguez restored parity for the home team in the 82nd minute.
Channiayin FC with two wins, two draws and a loss are in third place in the league table with eight points. Pune are placed sixth with five points.
Chennaiyin FC arrived here on the back of two successive victories against FC Goa and NorthEast United and the defending champions appeared good enough to continue with their winning run, thanks to a stunning strike from Jeje.
The Spanish coach was at his dramatic best on the sidelines but at the other end, it was the inclusion of Jeje in the starting line-up for Chennaiyin FC that should have made heads turn.
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Jeje was in superb form last season scoring six goals but this year the goals had dried up. Coach Marco Materazzi relegated him to the bench for the last two matches but decided to throw him into the starting mix due to his excellent record against Pune.
Jeje has scored twice, including the winner when the two teams last met and he was at it again on Sunday.
Bete tried to backtrack and rescue the situation but Jeje had put in enough power to carry the ball into the net.
Chennaiyin FC were extremely disciplined at the back, allowing very little room for Pune to have a clear look at the goal. The only time Pune managed to test their rivals was from a distance as Jonatan Lucca and Jesus Tato's efforts sailed just wide of the target.
The rebound fell kindly for Hans Mulder but, under pressure from Rahul Bheke, Mulder couldn't give the finishing touches.
Just when it seemed Chennaiyin FC would become the first team in this edition of ISL to notch a hat-trick of victories, Pune scored the equaliser.
It was a wonderfully taken free-kick from just outside the box by Anibal Rodriguez in the 82nd minute that finally overcame a resolute Chennaiyin defence and sailed past a diving Chennaiyin goalkeeper Duwayne Kerr.
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