Sharma collected 2-23 from eight overs, after the West Indies were sent in to bat on the occasion of the inaugural Test at Windsor Park here.
Praveen Kumar made the breakthrough for the Indians inside the first half hour when Test newcomer Kieran Powell was caught at second slip for three, playing defensively forward to a delivery that moved across him.
Sharma then struck twice in the space of 12 deliveries, leaving West Indies reeling on 35 for three.
He bowled Adrian Barath for 12, the opener attempting a hook at a short, rising delivery but diverting the ball into his stumps off the glove.
Sharma fortuitously captured his second scalp when Kirk Edwards, another Test debutant, was adjudged caught behind for six.
But television replays suggested that English umpire Richard Kettleborough may have erred in his decision, since the ball may have ricocheted from the helmet.
It was, however, a series-high 18th wicket for the beanpole Indian fast bowler.
For the remainder of the session the visitors met resistance, after Shivnarine Chanderpaul, not out on 11 on his record 133rd appearance for the West Indies, joined fellow left-hander Darren Bravo, not on 17.
Chanderpaul is now the most capped West Indies player in Tests.
India made one change to their line-up, with Munaf Patel replacing Abhimanyu Mithun, while West Indies dropped Lendl Simmons and Ramnaresh Sarwan to hand Test debuts to left-handed opener Powell and middleman Edwards.
India hold a 1-0 lead in the three-Test series following a 63-run victory inside four days in the first Test at Sabina Park in Jamaica and a draw in the second Test at Kensington Oval in Barbados.
The visitors will be looking to wrap up their second straight Test series victory over the West Indies in the Caribbean.
They are also bidding to create a piece of history by becoming the first Indian side to win a Test and one-day international series in the Caribbean.
Windsor Park is the 12th venue in the Caribbean to host a Test and 106th worldwide.
Copyright AFP (Agence France-Presse), 2011