After a barren first half, You Seungji put the Koreans ahead in the 47th minute with a immaculate penalty corner conversion.
But India replied back seven minutes later through a field effort from lanky Lokesh Thimmmana after he was set up by Naveen Antil's perfect cross from the sidelines of the circle.
However, thereafter the Koreans kept the Indian forwards under check with neat trap and fast attacks, stretching the game into extra time.
India had a chance to seal the match at the end of the first period of extra time, but Amit Rohidas once again faltered with his penalty corner flick.
But India found the winner in the second half of extra time from a counterattack when Akashdeep scored from inside the circle after receiving a pass from Lokesh.
The Indians, however, could have sealed the match much before if not for their sloppy forwards, who came close to scoring thrice -- 17th, 25th and 29th minutes -- in the first period.
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The Korean defence manned by skipper Yang Jihun, Choic Jihun and You Seungju stood like a rock of Gibraltar to deny the Indians any headway.
The Indians were also off-colour with penalty corner conversion as Korean goalkeeper Lee Seyoung thwarted all the three set pieces the defending champions earned in the match.
Korea too did not show any acumen in penalty corners as they wasted both the opportunities that came their way on fifth and 34th minutes.