India's record scorer Chhetri, 34, netted twice - his 66th and 67th strikes for his country - before Anirudh Thapa's first international goal and an effort from substitute Jeje Lalpekhlua put the result beyond doubt.
Teerasil Dangda, the lone survivor from Thailand's last Asian Cup appearance in 2007, briefly levelled the match in a first half his side edged, but Stephen Constantine's side were completely dominant after the break and deserving winners.
India had one draw and six defeats from their last seven Asian Cup games, but are now well placed at the top of Group A following a first win in the tournament since they were runners-up in 1964.
Thailand, meanwhile, have won just one of their last 21 Asian Cup games following the morale-denting defeat at Al Nahyan Stadium in Abu Dhabi.
They had made the better start and came close when Adisak Kraisorn forced a close-range save from India captain Gurpreet Singh Sandhu.
But, against the run of play, a controversial refereeing decision turned the game in India's favour. Ashique Kuruniyan had a shot saved by Chatchai Budprom and the ball rebounded off the arm of defender Theerathon Bunmathan, who was in close proximity.
That resulted in a spot-kick, from which the veteran Chhetri coolly sent Budprom the wrong way to earn a 27th-minute lead.
Bunmathan redeemed himself just six minutes later as his curling free-kick was headed in by Dangda over a poorly positioned Sandhu.
A back-and-forth clash saw Chhetri strike again just 55 seconds into the second half, firing a fine first-time strike from 18 yards into the top-left corner after Kuruniyan and Udanta Singh had set him up.
Chhetri headed just off target as he sought a hat-trick, but Thapa sealed victory after 68 minutes, producing a superb dinked finish after a neat assist from Singh.
Lalpekhlua was the next man to beat Budprom with 10 minutes left, converting Halicharan Narzary's pass to put India top of a pool that also contains hosts UAE and Bahrain.