Tendulkar, playing his 95th Test, departed edging an out-swinger from left-arm paceman Pedro Collins to wicketkeeper Ridley Jacobs.
This was the 10th time the 29-year-old fell without scoring and his fourth first-ball duck. The last time the 29-year-old suffered a first-ball demise was against Pakistan in 1999 when paceman Shoaib Akhtar claimed his wicket in Calcutta.
Tendulkar has scored 0, 0, 8 and 0 in his last four innings after hammering 117 for his 29th test century in the first innings at Trinidad last month to equal the achievement of Australian Don Bradman.
Dravid was batting on 86, with 14 boundaries, and captain Saurav Ganguly was on 41. The two raised 58 for the fourth wicket to rescue India after left-arm paceman Pedro Collins removed Jaffer (86) and Tendulkar off consecutive balls.
India had won the second test at Trinidad by 37 runs but West Indies hit back with a 10-wicket win at Barbados to level the series 1-1.
India’s start on Friday was in stark contrast to Barbados, where the visitors were bundled out for 102 in their first innings, with Jaffer and Shiv Sundar Das negotiating the four-pronged West Indian pace attack with ease after being asked to bat first.
Das fell for a 28-ball three when he dragged a wideish delivery from Collins, who finished with three wickets for 65, on to his stumps.
But Jaffer, who had struck 51 for his maiden half-century at Barbados, and Dravid dug in with a 155-run partnership to ensure the fiasco of the previous test was not repeated.
Jaffer, playing his fourth match, piled on the runs as he freely scored boundaries off paceman Cameron Cuffy and Collins.
He was, however, fortunate on 46, when he edged Cuffy just short of Brian Lara at first slip.
Jaffer raised his second successive 50, off 88 balls, flicking paceman Mervyn Dillon to the square leg fence for four.
He then drove Dillon to the mid-wicket fence and hit Collins through long-off for another of his 14 boundaries.
Dravid played the anchor role initially by keeping the scoreboard ticking in ones and twos but cut loose after settling in.
The Bangalore batsman, who had scored 144 in the first drawn test at Georgetown, got into his groove driving Collins and fast bowler Adam Sanford down the ground for fours.
He raised his 50, off 138 balls, driving Collins through extra cover for his eighth four.
But Collins pegged India back having Jaffer edge a ball that was angling away from him and then getting Tendulkar in almost identical fashion.
Captain Ganguly, the only Indian batsmen to put up any resistance at Barbados, again looked in prime form as he safely negotiated the attack, pulling Sanford over the mid-wicket fence for the day’s only six.
India had won the second test at Trinidad by 37 runs for their first victory in the Caribbean in over 26 years.
They beat Sri Lanka in 1993-94 but have not won a test series outside south Asia since defeating England in the 1985-86 season.
West Indies, who had lost six of their last seven tests before the Barbados match, are looking to bounce back from two straight Test series losses.
INDIA (1st innings)
S.Das b Collins 3
W.Jaffer c Jacobs b Collins 86
R.Dravid not out 86
S.Tendulkar c Jacobs b Collins 0
S.Ganguly not out 41
EXTRAS (lb-3 nb-6 w-1) 10
TOTAL (for three wickets, 90 overs) 226
FALL OF WKTS: 1-13, 2-168, 3-168
TO BAT: V.Laxman, A.Ratra, A.Kumble, Z.Khan, J.Srinath, A.Nehra
BOWLING: Dillon 22-6-46-0 (nb-2), Cuffy 20-4-40-0 (nb-1), Collins 21-5-65-3 (nb-2 w-1), Sanford 19-4-52-0 (nb-1), Hooper 5-2-11-0, Hinds 2-0-9-0, Sarwan 1-1-0-0.
WEST INDIES: C.Gayle, W.Hinds, R.Sarwan, C.Hooper, B.Lara, S.Chanderpaul, R.Jacobs, M.Dillon, A.Sanford, P.Collins, C.Cuffy.—Reuters