Chase, playing only his second Test match, came up with a resolute 137 off 269 balls and in the process raised three match-saving partnerships with his teammates.
The 24-year-old batsman batted through the day and became only the fourth West Indies player to score a hundred and claim a five-wicket haul in same match. He had returned figures of five for 121 in India's first innings.
West Indies began the day at a pitiable 48 for four but lost only two wickets in the entire fifth day, scuppering India's ambitions to take a 2-0 lead in the four-match series.
Chase joined overnight batsman Jermaine Blackwood (63) at the start of play in the morning and raised a 93-run stand for the fifth wicket to deny India much success.
As sun shone bright and sunny, the wicket eased out a lot and hardly offered any assistance to the Indian bowlers.
After Dowrich's dismissal, skipper Jason Holder joined his junior colleague and provided him tremendous support by hitting a fighting unbeaten 64, putting together a 103-run stand for the unconquered seventh wicket.
Chase's knock had 15 shots to the fence and one over the ropes while holder struck eight fours and six.
Only 29 overs remained in the last session of the match to be bowled as India looked to make use of the new ball. But they were never happy with the proceedings, complaining often to the umpires about the shape of the ball, even though the ball wasn't changed.
The spinners couldn't get much purchase from the pitch either, which was shorn of day five characteristics and the batsmen did not have much difficulty in negotiation the Indian bowling.
The two teams shook hands with 35 minutes left before the scheduled close of play.
(REOPENS DEL 20)
Skipper Virat Kohli (12) cover drove Lyon for a boundary through vacant cover region but then misjudged the turn once again that did him in.
He shouldered arms to a delivery from Lyon thinking it will be an off-break and the ball didn't turn enough hitting him in the middle and leg stump line.
Ajinkya Rahane's (17) torrid time during the current home season continued as he came down the track with intent to smother the spin but it was the straighter one that he missed.
Matthew Wade fumbled in the first attempt before effecting the stumping to leave India at 118 for 4.
When Nair joined Rahul, the two local lads looked comfortable during their 38-run stand.
He played a lovely back cut off Steve O'Keefe but then came down the track to a delivery that turned enough to beat the bat and was stumped by Wade.
India went into the break with scoreboard reading 168 for five. But once the tea break was over, Lyon went on a rampage as Indian innings folded without any resistance from the lower-middle order.
A sharp bouncy off-break saw Ravichandran Ashwin (7) glove one to David Warner at the backward short-leg.
Rahul, who had reached the 80s, was feeling a twitch in his shoulders as he tried to smack Lyon and O'Keefe with sweep shots.
Ravindra Jadeja (3) could have helped Rahul get a well-deserved hundred but a bat-pad catch went to the slip cordon and skipper Steve Smith successfully reviewed the appeal.
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