For the winners, the other two goals were scored by Nigerian striker Kalu Uche in the 16th and 23rd minute while Mohammed Rafi struck for the losing side in the 1st and 30th minute.
The win took David Platt coached Pune City past Chennaiyin FC as they are now on top of the eight-team league table with 12 points from six games with their fourth win.
It was perhaps the most entertaining match in the tournament, where the standard of football has not exactly been great.
The fortunes swung like a pendulum from the very first minute when Kerala striker Rafi scored his 3rd goal of the season just after kick off in the very first minute.
With Chris Dagnell essaying a neat cross from the wide right, Rafi positioned himself to perfection as he got the visitors lead in the opening minute of the match.
Shorey floated one from the left with Uche heading home as former India stopper Gourmangi Singh not in his position.
Within seven minutes, Pune made it 2-1 courtesy Shorey-Uche combine. It was Shorey, who weaved past a couple of Blasters men before unleashing a oerfect assist which the Nigerian tapped home from close range.
But Pune's joy was shortlived as Rafi got his fourth goal of the tournament, when Rafi headed him at stroke of half an hour as his nod first hit the right post and then trickled down towards left before entering.
The winner by Tuncay, came in the 72nd minute when Shorey again went down wide left to essay a cross which saw the former Fenerbahce and Middlesbrough striker outjump his marker to perfectly nod home.