Delhi took the lead through Kean Lewis (44th minute) but Pune turned the match around in second session with goals from Anibal Rodriguez (55th and 63rd), Mohammed Sissoko (62nd) and Lenny Rodrigues (90th).
An own goal from Pune player Eduardo Ferreira (79th) and Malsawmzuala's strike in the injury time kept Delhi in the hunt till the very end before losing the match at Shiv Chhatrapati Sports Complex Stadium at Balewadi.
The victory took Pune to the fourth spot from earlier sixth with 15 points from 11 matches, just two less than Delhi who could have virtually sealed their place in the play-offs with three points today.
Chennaiyin FC and Atletico de Kolkata, both out of the top four now, can move on top with victories tomorrow, while NorthEast United FC (11 points) and FC Goa (11 points) are still in the competition with three matches left to be played.
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In an exciting contest, Delhi goalkeeper Soren Porei was the hero for his team in the first 45 minutes after stopping a penalty from Mohammed Sissoko and blocking Momar Ndoye twice in a one-on-one situation.
The miss proved costly for Pune as they conceded a goal close to half time. Marcelinho's back-heel from just outside the box released Emerson Gomes de Moura whose pass inside the box gave Kean Lewis the space and time to slot it into the net in the 44th minute.
The goal was the 400th in the ISL and gave Delhi confidence that they can qualify for the semi-finals with three matches in hand but Pune struck in the 55th minute. A free kick from Jonatan Lucca found Anibal who rose high over two defenders and headed it into the far post.
Pune appeared to have wrapped up the game only a minute later as Anibal capitalised on a blunder from Delhi Dynamos. Goalkeeper Porei threw the ball away to Ruben Gonzalez who could not control it. Anibal picked it up and beat the goalkeeper at the near post with a lightning strike.
Florent Malouda had a hand in the second goal for Delhi as his shot across the goal hit defender Eduardo and sailed into the goal in the 79th minute. Any chance of a comeback was, however, snuffed out by Pune midfielder Lenny Rodrigues when he finished a pass from Lucca in the last minute of play.
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