Yuvraj had steered the visitors' chase with a brilliant 93 but he was last out as India was bowled for 197 off 49.4 overs.West Indies totaled 198 for nine off 50 overs on the back of a gritty, unbeaten 98 from Ramnaresh Sarwan, who was named Man-of-the-Match.
India's bowlers were impressive with the new-ball pair of Ajit Agarkar (two for 25) and Irfan Pathan (3-45) setting back West Indies early.
Off-spinners Ramesh Powar (2-38) and Harbhajan Singh (1-32) helped maintain India's stranglehold throughout the innings.
West Indies' attack showed similar incisiveness as India attempted to stretch its world record of successful chases to 18.
Left-arm seamer Ian Bradshaw led the way by removing captain Rahul Dravid (11) and fellow opener Virender Sehwag (12) as India slipped to 37 for two.
Fellow pacers Fidel Edwards and Jerome Taylor also chipped in with vital middle-order wickets.
Irfan Pathan (14) dragged a catch to mid-on and Mohammad Kaif (4) top-edged a pull as India dipped to 60-4.
Yuvraj, who lashed eight fours and a six off 121 balls, shared a restorative fifth-wicket stand of 64 with fellow left-hander Suresh Raina. The 19-year-old Raina compiled 27 off 55 balls before the West Indian slow bowlers also made their mark.
Marlon Samuels, who ended with 2-30, claimed Raina to a catch at long-off.
Taylor forced the dangerous Mahendra Dhoni (2) to drag onto his stumps and Bradshaw took a brilliant return catch to claim Agarkar (2) as West Indies took control at 134-7.
But Yuvraj forged another busy partnership of 43 with Ramesh Powar to set up a thrilling finale.
There were 22 runs needed off 22 balls when Samuels struck another decisive blow as Powar holed out to long off for 12.
Gayle grabbed a diving, one-handed caught and bowled to remove Harbhajan for one at 187-9. It left Yuvraj and last man Munaf Patel with 12 to get from 11 balls.
Yuvraj seemed to have blasted India home with two boundaries off successive deliveries in Bravo's final over.
But the 22-year-old Bravo turned from villain to hero with an audacious slower ball yorker which clipped the leg stump of Yuvraj as he played across the line.
Bravo was swamped by his teammates and the crowd of about 8,000 waved flags and danced around in delight.
Earlier, Agarkar set back West Indies in the second over as he got Gayle to edge to Dhoni.
Four balls later, the score was 1-2 when Pathan claimed Runako Morton leg before wicket to an inswinger.
Sarwan and Lara added 23 for the third wicket as they tried to rebuild but two more quick wickets further flattened West Indies.
Lara made 14 before he chased a wide ball from Pathan and was caught by opposite skipper Dravid at slip.
Shivnarine Chanderpaul (10) followed at 43-4 as he cracked a long-hop from Harbhajan Singh straight to point.
Sarwan and Samuels labored in a face-saving partnership of 60 which spanned 16 overs.
Samuels, whose 19 took 53 balls, eventually edged to Dhoni off Yuvraj's spin.
Bravo followed for a duck, clipping Powar to a diving Raina at midwicket.
Carlton Baugh injected some life in the innings with 21 off 17 balls and Sarwan accelerated toward the end as West Indies scored 71 runs off the last 10 overs.
The 25-year-old Sarwan, in his 99th match, struck seven fours and one six but just missed out on reaching his third one-day century.
Scoreboard
WEST INDIES:
C.H. Gayle c Dhoni b Agarkar 0
R.S. Morton lbw b Pathan 1
R.R. Sarwan not out 98
B.C. Lara c Dravid b Pathan 14
S. Chanderpaul c Kaif b H. Singh 10
MN. Samuels c Dhoni b Y. Singh 19
D.J.J. Bravo c Raina b Powar 0
C.S. Baugh c Pathan b Powar 21
I.D.R. Bradshaw c H. Singh b Pathan 12
J.E. Taylor c Dhoni b Agarkar 9
F.H. Edwards not out 1
EXTRAS (LB-2, W-8, NB-3) 13
TOTAL (for nine wkts, 50 overs) 198
FALL OF WKTS: 1-1, 2-1, 3-24, 4-43, 5-103, 6-105, 7-143, 8-163, 9-197.
BOWLING: Irfan Pathan 9-2-45-3 (1nb, 4w); Agarkar 10-2-25-2 (1w); Harbhajan Singh 10-0-321; Munaf Patel 7-1-39-0 (2nb, 1w); Powar 10-0-38-2 (2w); Yuvraj Singh 4-0-17-1.
INDIA:
V. Sehwag c sub (D.R. Smith) b Bradshaw 12
R. Dravid c Baugh b Bradshaw 11
Irfan Pathan c Samuels b Edwards 14
Yuvraj Singh b Bravo 93
Mohammad Kaif c sub (D.R. Smith) b Taylor 4
S.K. Raina c Chanderpaul b Samuels 27
M.S. Dhoni b Taylor 2
A.B. Agarkar c and b Bradshaw 2
R.R. Powar c Taylor b Samuels 12
Harbhajan Singh c and b Gayle 1
Munaf Patel not out 2
EXTRAS (LB-4, W-8, NB-5) 17
TOTAL (all out, 49.4 overs) 197
FALL OF WKTS: 1-25, 2-37, 3-51, 4-60, 5-124, 6-130, 7-134, 8-177, 9-197.
BOWLING: Edwards 7-2-19-1 (2nb, 2w); Bradshaw 10-0-33-3 (3nb, 1w); Taylor 9-0-49-2 (1w); Bravo 3.4-0-29-1 (1w); Gayle 10-0-33-1 (2w); Samuels 10-0-30-2 (1w).
RESULT: West Indies won by one run.
UMPIRES: B.R. Doctrove (West Indies) and Asad Rauf (Pakistan).
TV UMPIRE: N. Malcolm (West Indies).
MATCH REFEREE: B.C. Broad (England).
MAN-OF-THE-MATCH: Ramnaresh Sarwan.
NEXT MATCH: At Basseterre (St Kitts) on Tuesday.—Agencies