Without a score of note in his comeback series, Ambris tried to make his mark, carving out four fours off 95 balls in almost two hours at the crease.
After being bowled out cheaply in the first session and managing only a lead of 56 runs, the Indian bowlers riding on Umesh Yadav's brilliant spell roared back to knock the West Indies over for a paltry 127 in their second essay.
The hosts' control of the match was threatened early on Sunday as their tail-end collapse saw them post 367 all out under pressure from Jason Holder (5-56), but the Windies' failure to capitalise with the bat proved costly.
Team India thumped the Windies sensationally in the second and final Test to pocket the series by 2-0. The 18-year-old Shaw hit the winning boundary as the world's top Test side registered their 10th successive series triumph on home soil.
Shaw fell to left-arm spinner Jomel Warrican, after hitting 11 fours and a six, and Cheteshwar Pujara went for 10 in the very next over off seamer Shannon Gabriel.
India dominated the last two sessions of the third day's play in the second and final Test match to crush West Indies by 10 wickets and complete a series whitewash easily on Sunday.
Sunil Ambris topscored with 38 and Shai Hope got 28, but West Indies never recovered from six for two in the fourth over after losing openers Kraigg Brathwaite and Kieran Powell, both without scoring.
Ambris and Holder (19) delayed the inevitable after tea, adding 38 for the seventh wicket to keep India wicket-less for almost 40 minutes.
Umesh never allowed partnerships to flourish in the West Indies first innings and finished with figures of 6 for 88.
"It's a tough series and we didn't play our best cricket. We need to learn and learn quickly and understand", added Holder, who has captained West Indies in 27 of his 35 Tests.
Earlier Yadav, who lost his pace partner in debutant Shardul Thakur due to a groin strain on day one, picked all the three West Indian wickets to fall in the morning after the tourists started the day on 295-7.