The 22-year-old off-spinner plotted a sensational West Indian collapse, taking 7-48, on a turning track.
Leg-spinner Anil Kumble (3-50) took the remaining wickets as India posted their first innings win over the West Indies in 76 Tests.
It was an easily forgettable 100th Test for West Indies skipper Carl Hooper as his team crashed to 188 on the fourth day after having conceded a first-innings lead of 300.
His counterpart, Saurav Ganguly, was all smiles after leading India to their 12th win since taking over the captaincy from Sachin Tendulkar two years ago.
Ganguly is now just two victories short of equalling former captain Mohammad Azharuddin’s Indian record of 14 Test wins.
It was also India’s ninth Test victory over the West Indies and the first at this venue since 1994-95.
The West Indies found the spin-dose too bitter to swallow on the fourth-day pitch at the Wankhede Stadium, losing their last nine wickets for a meagre 83 to a combination of tight bowling and irresponsible shots.
The tourists were 105-1 before being all out 51 minutes after lunch to trail 1-0 in a three-match series.
Left-handed Shivnarine Chanderpaul yet again played a defiant knock, scoring an unbeaten 36 in his team’s dismal batting performance for the second successive innings in the match.
The West Indies had crashed to left-arm bowler Zaheer Khan’s pace in the first innings and to the spin-twins in the second, with Harbhajan finishing with his 10th haul of five or more wickets in a innings in 29 Tests.
Harbhajan’s turn and Kumble’s bounce made life miserable for the West Indian batsmen, who just could not read the spin.
Ganguly maintained pressure on the tourists from the first over through the spin-duo, sometimes keeping as many as five fielders close to the bat after using pace for just one over.
Harbhajan, whose Saturday’s spell read 19.3-9-24-6, provided the breakthrough in the morning’s sixth over when he had left-handed opener Chris Gayle by Ganguly at wide mid-off.
Gayle (42) added eight to his overnight score of 34 before uppishly driving the off-spinner. The Indian skipper did well to keep his eye on the ball despite Sanjay Bangar almost running into him from mid-off.
Ramnaresh Sarwan (17) paid the penalty of driving Kumble away from the body and was caught by Sachin Tendulkar in the covers after adding eight to his overnight score.
Hooper walked in to bat in overcast conditions, praying for rain in his milestone Test as his team had been reduced to 107-3 after resuming at 91-1.
Hooper, one of the best batsmen of spin bowling, failed to live up to his reputation as he offered a simple return catch to Harbhajan after contributing one to leave his team struggling at 110-4.
The lower-order batsmen also failed to cope with spin as Kumble had Ryan Hinds and Ridley Jacobs caught by close-in fielders off successive deliveries to reduce the tourists to 117-6.
Mahendra Nagamootoo left alone the hat trick ball going down the leg-side and then was lucky to survive on five. He mistimed a drive off Harbhajan, but Bangar collided with Kumble at mid-off and a simple catch was dropped.
Luck deserted Nagamootoo 13 runs later as he was caught by Ganguly at first slip off Harbhajan, who then had Mervyn Dillon caught by Rahul Dravid in the slips in the same over.
Harbhajan finished the match when he dismissed Pedro Collons and Cameron Cuffy in the post-lunch session.
INDIA (1st Innings) 457 (V. Sehwag 147, R.S. Dravid 100 retired hurt).
WEST INDIES (1st Innings 157 (S. Chanderpaul 54; Zaheer Khan 4-41, A.R. Kumble 4-51).
WEST INDIES (2nd Innings, overnight 91-1):
C.H. Gayle c Ganguly b H’bhajan 42
W.W. Hinds b H’bhajan 40
R.R. Sarwan c Tendulkar b Kumble 17
S. Chanderpaul not out 36
C.L. Hooper c and b H’bhajan 1
R.O. Hinds c Sehwag b Kumble 2
R.D. Jacobs c Ganguly b Kumble 0
M.V. Nagamootoo c Ganguly b H’bhajan 18
M. Dillon c Dravid b H’bhajan 0
P.T. Collins c Dravid b H’bhajan 8
C.E. Cuffy c and b H’bhajan 0
EXTRAS (B-8, LB-15, NB-1) 24
TOTAL (all out, 68.3 overs) 188
FALL OF WKTS: 1-60, 2-105, 3-107, 4-110, 5-117, 6-117, 7-158, 8-158, 9-184.
BOWLING: Srinath 4-2-19-0 (1nb); Zaheer Khan 4-0-26-0; Bangar 6-1-20-0; Harbhajan Singh 28.3-12-48-7; Kumble 25-8-50-3; Tendulkar 1-0-2-0.
RESULT: India won by an innings and 112 runs.
UMPIRES: E.A.R. de Silva (Sri Lanka) and D.R. Shepherd (England).
TV UMPIRE: I. Sivaram.
MATCH REFEREE: M.J. Procter (South Africa).
MAN-OF-THE-MATCH: Virender Sehwag.
SECOND TEST: Chennai, Oct 17-21.
THIRD TEST: Kolkata, Oct 30-Nov 3.—AFP/Reuters