The visitors scored through Nicolas Velez (4'), Diomansy Kamara (18') and Andre Bikey (43') while Pune struck twice courtesy James Bailey (8') and Adrian Mutu (86').
With the win, the Cesar Farias's side have moved to the fourth spot in the points table and would now hope Pune City win their last league game against Chennaiyin FC for them to secure a semifinal spot.
NorthEast have finished their campaign with 20 points while Pune City have eliminated from the competition.
It only took four minutes for Pune City to take the lead but the away team equalised in quick time.
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It was an eventful first half with NorthEast regaining their lead in the 18th minute from a quick counter-attack. Mendy found Velez who crossed across the face of goal where Kamara found space and time at the far post to tap the ball into an empty net.
In the second session, Pune City stepped up their attack and pressed more men forward but the visitors had nothing to show apart from a trademark Adrian Mutu free-kick in the 86th minute. The goal did not make much of a difference as NorthEast defended their lead to stay alive in the league.
Pune City, who led the ISL table at the start, ended their league engagements without a single away win.