Koo Ja-cheol and substitute Son Heung-min also got on the scoresheet for the Taeguk Warriors while Sunil Chhetri converted a 12th-minute penalty for Bob Houghton's men.
But Korea will rue a plethora of missed chances as Australia's 1-0 victory over Bahrain condemned them to second place in Group C on goal difference to set up a mouth-watering last eight clash with Iran.
It took just six minutes for Korea to break the deadlock. Lee Chung-yong's cross was pushed into the air by keeper Paul Subrata and Ji was on hand to head home unchallenged from six yards.
Three minutes later, they doubled their lead. Cha Du-ri's centre from the right was not cleared properly and Ji cushioned a neat header into the path of Koo, who rounded Subrata for his fourth goal of the tournament.
India pulled a goal back in the 12th minute when Kwak Tae-hwi climbed all over the back of Chhetri in the box and the striker picked himself up to send Jung Sung-ryong the wrong way from the spot.
Subrata kept out Koo's header from Lee Chung-yong's cross in the 20th minute before Kwak met Ki Sung-yeung's corner but saw his powerful header cleared off the line.
Korea then crafted a superb third goal in the 23rd minute when Koo held off a defender on the edge of the box before releasing Ji with a delightful little reverse pass and the striker lifted the ball over Subrata for his second of the game.
Ji was then left wondering how he did not complete his hat-trick 10 minutes before the break.
Subrata let Ki's corner squirm through his hands and it fell to the Chunnam player six yards out. His initial shot was blocked by Syed Rahim Nabi and when the ball rebounded to Ji, his second effort hit the prone Indian forward. Again it came back to Ji but his third shot was blocked on the line by Surkumar Singh.
As half-time approached, Subrata pushed away Lee Chung-yong's low shot, parried a powerful effort from Ji and got down well low to his left to keep out Kwak's header all in the space of a couple of minutes.
Korea continued to carve India apart in the second-half but were unable to convert their superiority into goals.
Lee Chung-yong sidefooted wide from eight yards and Subrata did well to stretch out a leg and deny Son.
Son came even closer to adding to Korea's tally in the 64th minute when Lee's low cross reached the substitute at the back post but his first-time shot hit the upright and India cleared. From the resulting corner, Deepak Kumar Mandal cleared Hwang Jae-won's header off the line.
Subrata brilliantly turned Lee Yong-rae's free-kick behind at full stretch and Korea continued to spurn opportunities as they were at times guilty of trying to walk the ball into the net.
Ji fired over from 12 yards with a sea of defenders in front of him after Subrata had been caught out of position before Korea finally scored their fourth goal with nine minutes to go.
Koo played in Son down the left hand side of the box and he rifled the ball into the back of the net via the underside of the bar.