A 82nd minute goal from captain Henrique Sereno was enough for the former ISL champions to win their second match on the trot at the Balewadi Stadium.
After a cagey opening 15 minutes, Pune took control but could not create any clear-cut goal scoring chances. Some of their best chances of the half came from set plays.
Marcos Tebar's free-kick in the 19th minute was headed down by a Pune player to Alfaro, who in turn passed in on to Rafael Lopez. But the Spanish defender's side-footed shot went inches wide of the Chennaiyin goal.
After stringing together a few passes in midfield, Inigo Calderon sent in a delightful cross into the box for Nelson to connect. The Dutchman's diving header, however, was cleared by Rafael.
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Both sides started the second half much like the first -- unable to create chances going forward.
In the 60th minute, Pune goalkeeper Vishal Kaith almost gifted a goal to John Gregory's side. The goalkeeper came out of his box to collect a harmless-looking cross from Jerry Lalrinzuala but could only palm it in the path of midfielder Francisco Fernandes.
At the other end, Alfaro should have given Pune the lead in the 77th minute. After finding himself clear on goal with only the goalkeeper to beat, the Uruguayan slashed the ball over the crossbar.
It looked like both sides would settle for a point each but there was a twist in the tale. With just eight minutes left for the final whistle, Sereno gave Chennaiyin FC the lead.
The defender rose above everyone else to thump Gavilan Martinez's corner past the FC Pune City goalkeeper.