Sangita scored in the 55th and 58th minutes after Ritu had put India ahead in the 45th minute in the bronze-medal play-off.
The two teams played out a goal-less first half, with India content with dropping deep and relying on the counter to create opportunities.
Korea earned several penalty corners but failed to convert from any, as India's defence closed them down perfectly.
The best chance of the half, however, fell to India as a defensive mistake in Korea's circle saw the ball came to Sangita Kumari who took a shot across the goal with Mahima also waiting for an opportunity. The weight on the pass was too much though as the chance went wide.
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The Indian eves kept applying pressure and in the 55th minute, Lalremsiami showed great vision to send an inch perfect pass to Sangita, who cut past two defenders to slot the ball into the goal and extend India's lead.
The third goal came off a similar route, Sangita scoring her second of the game in the 58th minute.
For their creditable bronze-winning performance, Hockey India announced cash rewards of Rs 1 lakh for each player and Rs 50,000 for each of the support staff.
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