Chase scored his maiden Test fifty (70 batting) at an opportune time for the troubled hosts as he weaved together a 93-run stand with Blackwood (63) before spinner R Ashwin removed the latter.
Chase (122 balls, 9 fours, 1 six) found another solid support in Shane Dowrich who was batting at 33 in an unbeaten 74 run stand for the sixth wicket as a bright sunny day made conditions better for batting at Sabina Park.
Starting at overnight 48 for four, Chase and Blackwood came out with a plan to defy the Indian bowlers. There had been no rain since play on day four had been called off and not a cloud was in sight today.
The visitors started off with Mohammed Shami (2/53) and Amit Mishra (1-56), but Blackwood attacked them both and hit them out of the attack.
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Ishant Sharma (1/34) and Umesh Yadav (0/21) were then deployed, but Blackwood continued attacking them too. The former bowled a bit wider outside of the off-stump in a bid to keep things tight, while Yadav used the short-ball approach against him.
The duo put 50 off just 54 balls and it seemed as if for once the hosts batting would come good. Ashwin (1/49) then was finally introduced into the attack in the 28th over of the innings, with skipper Virat Kohli opting to hold him back earlier in the session.
Blackwood hit a straight six in his second over but Ashwin got his revenge as he squeezed the batsman for runs bowling from round the wicket. The plan worked and Cheteshwar Pujara too a brilliant diving catch at forward short leg in the 34th over to send Blackwood back to the pavilion.
The Indian bowling didn't really trouble the duo as they brought up the 50-partnership off 82 balls, and the 200-mark came up for the West Indies in the 50th over. Yadav and Shami did get the ball to reverse later in the session, but couldn't get another success before the lunch break as the two batsmen looked comfortable at the crease.