With this victory, India would now play champions Australia in the last eight on March 24 in Ahmedabad while West Indies would face Pakistan in their quarterfinal clash.
Chasing 269, West Indies lost the plot after fine start as they kept losing wickets at regular intervals against India.
Yuvraj Singh struck again to dismiss seamer Andre Russell as West Indies lost four wickets in no time and were reduced to 165 for 7 from 154 for 3 in the period of five overs.
West Indies skipper Darren Sammy couldn't stay for long in the middle as he got run out in quest of a cheeky single.
Yuvraj Singh also came to the fore, after his fine stint with the bat, to dismiss Devon Thomas. Thomas was stumped by skipper MS Dhoni.
Zaheer Khan gave India crucial breakthrough against West Indies as he dismissed Devon Smith, who scored 81 off 97 balls, to break the vital 63-run stand between Smith and Ramnaresh Sarwan.
Harbhajan Singh got rid of dangerous Kieron Pollard cheaply soon after Smith's dismissal to reduce West Indies to 157 for four.
Suresh Raina accounted Darren Bravo's dismissal to break the crucial partnership between Bravo and Devon Smith.
Opener Devon Smith, who slammed his second fifty in the 2011 World Cup, kept the scoreboard ticking alongwith Darren Bravo as the duo added 57 runs for the second wicket after losing Edwards early.
Off-spinner R Ashwin opened the account for India as he trapped West Indies opener Kirk Edwards in front of the wicket.
Earlier, Yuvraj Singh's maiden World Cup century was the cornerstone of India's 268 all out against the West Indies but the host nation lost their last six wickets for just 36 runs.
Fast bowler Ravi Rampaul marked his World Cup debut with a career-best five for 51 which surpassed his 4-37 against India in Kingston in June 2009 -- the last time the West Indies beat a leading nation in a one-day international.
Yuvraj, who had already scored three fifties this tournament, made 113 to help revive a 38,000 capacity Chidambaram Stadium crowd stunned into silence by the early loss of Sachin Tendulkar.
Left-hander Yuvraj and Virat Kohli (59) shared a third-wicket stand of 122 after India were reduced to 51 for two following an early double strike by Rampaul, in for Kemar Roach, which included the prize scalp of Tendulkar.
India had already booked their place in the quarterfinals and many fans at the Chidambaram Stadium had hoped to witness cricket history by seeing Tendulkar score his 100th international century.
But Rampaul had Tendulkar, undone by a lifting delivery, caught behind for just two off the last ball of the first over.
Australian umpire Steve Davis rejected Rampaul's raucous appeal but a sporting Tendulkar walked off anyway.
Yuvraj was dropped twice by West Indies captain Darren Sammy -- once on nine at backward point and on 13 when the medium-pacer failed to hold an equally difficult return chance.
He piled on the agony for Sammy by striking him for two sixes.
Kohli offered sound support before he was bowled aiming across the line by Rampaul.
Yuvraj went to 96 by sweeping leg-spinner Davendra Bishoo for a boundary before a single off Kieron Pollard saw him to his hundred.
He was out caught and bowled by Pollard just before India were obliged to take the batting powerplay in the 45th over.
This again caused problems for India, with four wickets falling for 28 runs.
