The 33-year-old batsman reached a chancy 100 with a single off the last ball of the innings, helping the home team to pile up 341-3 after being asked to bat first.
The visitors were bowled out for 181 in 41.4 overs in reply, never really recovering after being reduced to five for 83.
Marlon Samuels struck his second consecutive fifty (55) and added 65 for the sixth wicket with wicket-keeper Denesh Ramdin (40), but the target was beyond reach for West Indies.
India's first one-day series victory since their 5-1 home triumph over England last April should boost their morale in the build-up to the World Cup.
Tendulkar was man-of-the-match and series after his 76-ball knock featuring 10 fours and a six. He added 118 for the third wicket with skipper Rahul Dravid (78) after the latter raised 101 runs for the second wicket with opener Saurav Ganguly (68).
Tendulkar, reprieved twice late in his innings, added 75 for the unbroken fourth wicket with Mahendra Dhoni (40).
Tendulkar, who hit a fifty in the previous match, displayed pristine form and was particularly severe on left-arm paceman Ian Bradshaw, hitting him for three boundaries in a row.
Tendulkar was let off on 85 and 91, skipper Brian Lara first letting a catch slip through his hands at cover before he was again dropped off Samuels.
Ganguly showed good touch to hit eight fours and a six from 82 balls until he was stumped against off-spinner Chris Gayle.
Dravid reached his second consecutive fifty with seven fours before he was caught in the deep off Samuels.
Ajit Agarkar dented West Indies' hopes for a good start when he bowled Gayle for six.
Left-arm paceman Zaheer Khan removed in-form Shivnarine Chanderpaul for 14 before Lara (3) and Simmons (4) were run out.
Samuels, who made 98 in the three-wicket victory in Chennai, and Ramdin stopped the rot before both fell in the space of five runs.
Scoreboard
INDIA:
A.R. Uthappa c Gayle b Powell 28
S.C. Ganguly st Ramdin b Gayle 68
R. Dravid c Simmons b Samuels 78
S.R. Tendulkar not out 100
M.S. Dhoni not out 40
EXTRAS (LB-14, W-9, NB-4) 27
TOTAL (for three wkts, 50 overs) 341
FALL OF WKTS: 1-47, 2-148, 3-266.
DID NOT BAT: Yuvraj Singh, Irfan Pathan, A.B. Agarkar, Zaheer Khan, Harbhajan Singh, A. Kumble.
BOWLING: Powell 8-0-68-1 (1nb, 4w); D.R. Smith 8-0-49-0; Emrit 9-0-65-0 (2nb, 1w); Samuels 9-0-51-1; Gayle 8-0-34-1 (1w); Bradshaw 8-0-60-0 (1nb, 3w).
WEST INDIES:
S. Chanderpaul c Harbhajan b Zaheer 14
C.H. Gayle b Agarkar 6
D.S. Smith c Yuvraj b Pathan 24
M.N. Samuels c Pathan b Kumble 55
B.C. Lara run out 3
L.M.P. Simmons run out 4
D. Ramdin c Kumble b Harbhajan 40
D.R. Smith lbw b Kumble 0
R.R. Emrit c Uthappa b Agarkar 13
I.D.R. Bradshaw not out 14
D.B. Powell c sub (Raina) b Yuvraj 1
EXTRAS (LB-3, W-4) 7
TOTAL (all out, 41.4 overs) 181
FALL OF WKTS: 1-10, 2-32, 3-65, 4-72, 5-83, 6-148, 7-153, 8-155, 9-180.
BOWLING: Agarkar 9-0-40-2 (2w); Zaheer Khan 6-1-21-1; Irfan Pathan 7-0-43-1 (2w); Harbhajan Singh 8-1-30-1; Kumble 7-1-27-2; Yuvraj Singh 4.4-0-17-1.
RESULT: India won by 160 runs.
UMPIRES: A.M. Saheba (India) and B.F. Bowden (New Zealand).
TV UMPIRE: S.L. Shastri (India).
MATCH REFEREE: A.G. Hurst (Australia).
MAN-OF-THE-MATCH: Sachin Tendulkar.
MAN-OF-THE-SERIES: Sachin Tendulkar.
FIRST MATCH: Nagpur, India won by 14 runs.
SECOND MATCH: Cuttack, India won by 20 runs.
THIRD MATCH: Chennai, West Indies won by three wickets.—Agencies