The 38-year-old was 33 not out, with Rahul Dravid on 30 not out, as India finished the day in New Delhi on 152-2. The hosts require another 124 runs for the victory.
Tendulkar came to the crease with India on 95-2 after the West Indies had been bowled out for 180. He is the leading scorer in Tests on 15,005 runs, with Dravid second on 12,859 runs.
Off-spinner Ravichandran Ashwin claimed six West Indies wickets, following three in the first innings, to finish with 9-128 on his Test debut.
The teams are scheduled to play three Tests and five one- day matches.
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