Raina (82) and Harbhajan (70) shared a boundary-studded seventh-wicket stand of 146 in two hours that revived the visitors from the crisis of 85-6 just after lunch.
Fidel Edwards led the hosts' bowling attack with 4-59 while fellow fast bowler Ravi Rampaul (3-59) and leg-spinner Devendra Bishoo (3-75) were also impressive.
The West Indies cautiously replied to be 34-1 from 20 overs at stumps. Lendl Simmons (3) was the batsman to fall, while Adrian Barath (26) and Ramnaresh Sarwan (2) will resume.
India, after choosing to bat, were quickly in trouble as Rampaul removed their inexperienced openers inside the first hour.
Murali Vijay (8) departed in the fourth over, slicing a leaden-footed drive off the front foot to backward point where Bishoo clung on to a juggled catch.
Left-hander Abhinav Mukund, one of three debutants for India, did not fare much better. He compiled 11 before he lost his leg stump as he inside edged a drive at Rampaul at 30-2.
The seasoned pair of Rahul Dravid and VVS. Laxman, carrying the burden of India's batting in this series in the absence of the injured openers Virender Sehwag and Gautam Gambhir, and the resting Sachin Tendulkar, rebuilt the innings with a third wicket stand of 34.
But the West Indies struck twice just before lunch to stun the No 1-ranked test team.
Laxman (12), dropped by a diving Rampaul at mid-on when on 5, played across the line of Bishoo's first delivery and edged to West Indies captain Darren Sammy at slip.
Virat Kohli, the second of the Indian debutants, lasted just 10 deliveries. He got off the mark by clipping an Edwards full toss to fine leg but fell in the last over before lunch, edging the same bowler through to wicket-keeper Carlton Baugh.
Bishoo further wrecked the innings on resumption as he added the prized scalps of Dravid and captain Mahendra Singh Dhoni.
Dravid, after cracking seven fours in his 40, fell in similar fashion to Laxman, pouched by Sammy at slip as he drove.
Dhoni followed for a duck, deflecting to gully as he stretched forward defensively.
"I feel really good," Bishoo said. "Watching them play all those years of cricket and bowling that well to them; it's a good opportunity and I enjoyed it."
Harbhajan, who hit two centuries in a series against New Zealand last year, signalled his intent early and was quickly into boundary-hitting mode against Bishoo.
Raina took a little longer to settle in but he, too, played some majestic strokes against all the bowlers, mainly meaty drives down the ground and through the off side.
The West Indies' best chances to dislodge the pair came through run out opportunities.
Raina was on 25 when Darren Sammy, in his follow through, missed at the bowler's end with Raina stranded after being sent back late by Harbhajan.
Then Harbhajan was one short of 50 when Adrian Barath's throw from backward point missed its mark.
It took a dazzling piece of fielding to break the partnership, with Bishoo grabbing a magnificent running catch at square leg as Harbhajan miscued a hook at Edwards.
Harbhajan struck 10 fours and a six off 74 balls.
Edwards soon added the wickets of Praveen Kumar (4) and Amit Mishra (6) to tip the balance back to the home team. Kumar was lbw playing across the line, while Mishra fended a bouncer to first slip.
Rampaul returned to end the innings as Bishoo hauled in another fine catch at deep square leg to deny Raina a second test ton. Raina cracked 15 boundaries off 115 deliveries.
The West Indies were becalmed in the final hour and a-half against a disciplined Indian attack.
Ishant Sharma claimed Simmons (3) midway through the session, pouched at short-leg by Murali Vijay off bat and pad.
