The visiting team took the lead through Balwant Singh in the 32nd minute, who became the first Indian to score in the inaugural tournament.
Brazilian Elano, Chennai's 'marquee' player doubled their lead in the 42nd minute with a well taken free-kick as they went into the break with a comfortable 2-0 lead.
Gregory Arnolin reduced the margin for the hosts on 65th minutes but couldn't muster the equaliser despite coming close on several occasions.
Goa made a lively start to the game in front of strong home support.
Portuguese Edgar Marcelino along with 'icon' Robert Pires was at the heart of Goa's attacks with some incisive passing.
The Chennaiyin defence soaked up the pressure well and went ahead after the half-hour mark.
Elano latched onto a poor clearance and made his way into the box before laying the ball to striker Balwant who converted the chance.
A foul on the edge of the box ten minutes later gave Elano a perfect opportunity to unleash a swerving free-kick, that went in to put his team 2-0 up.
Goa started with a lot of purpose after the break and eventually clawed their way back in the 65th minute when two defenders combined to get the home team on the score sheet.
Youness Bengelloun's knockdown from an over-hit cross was a perfect cut-back for fellow central defender Gregory Arnolin to tap in from close range.
Goa pushed on in search of an equaliser, with substitute Clifford Miranda coming close with a audacious attempt of scoring directly from a corner kick.
Chennaiyin keeper Emiliano Bracigliano pulled off a fantastic save to deny Randy Martins and held on for a win.