The former captain specially congratulated India skipper Virat Kohli, head coach Anil Kumble and seasoned off-spinner Ravichandran Ashwin.
Ashwin starred with the ball claiming an impressive seven-wicket haul to dismantle the hosts batting line-up on Sunday.
This was India's biggest margin of victory outside the sub-continent.
Congrats to @imVkohli led #TeamIndia on a wonderful win. Great performance @ashwinravi99 & wonderful debut for @anilkumble1074. Keep it up! Tendulkar tweeted.
India posted a mammoth 566/8 declared in the first innings, thanks to Kohlis 200 and Ashwins 113, while the West Indies were bundled out for 243 and 231 in first and second innings respectively.
Indias leg-spin legend Kumble took over as the head coach of the national team ahead of the Test series.
All-rounder Irfan Pathan also congratulated Ashwin.
Scoring 100 n taking 5-for in the same game is so special, enjoy every bit of it mate. very well done @ashwinravi99, Irfan wrote on Twitter.
The second Test begins in Kingston on July 30.
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