South Korea finished on seven points, as did Australia, which beat Bahrain 1-0 to win the group on goal difference.
South Korea scored twice within the first nine minutes, Ji finding the net in the sixth and Koo Ja-cheol doubling the lead three minutes later.
India pulled one back through Sunil Chhetri's penalty in the 12th, before Ji restored South Korea's two-goal cushion in the 23rd.
Substitute Son Heung-min scored in the 81st after South Korea had wasted a host of chances in the second half. Koo also set up two goals.
The match began in pouring rain and the goals poured in, too.
South Korea led 1-0 after Lee Chung-yong crossed from the right, India goalkeeper Subrata Paul made a poor interception and Ji headed inside the far post.
Three minutes later, another mistimed clearance by the Indian defense from a cross by Cha Du-ri allowed Koo to head the ball to Ji, who nodded it back for Koo to fake the goalkeeper and slot home his fourth goal of the tournament.
India gave its supporters something to cheer about soon after, forward Sunil Chhetri being brought down by big defender Kwak Tae-hwi to earn a penalty. The forward, who plays for Kansas City Wizards, converted the penalty himself to cut India's deficit.
Ji nearly got another but Subrata stopped his header, then Kwak had his header cleared off the line as the more athletic South Korea piled on the pressure.
Ji notched his second goal after collecting a good pass from Koo to beat Subrata from point-blank range.
India's shaky defense nearly allowed Ji another goal after Subrata had fumbled a cross, but two clearances were made on the line.
Subrata distinguished himself, however, with two good saves late in the first half.
He also foiled Manchester United captain Park Ji-sung by sticking out his right leg to stop a shot in the second half, and then blocked a close-range header from Son Heung-min.
Subrata's best save came when he turned away a free kick attempt by Lee Yong-rae in the 66th.
South Korea kept squandering chances, Ji even missing an empty net with Subrata stranded. But Son scored his goal by slamming the ball into the roof of the net after a pass from Koo.
India finished the tournament with three losses in three games, having conceded 15 goals.
