India's arch-rivals Pakistan have already made it to the last four stage from Pool A after beating hosts Malaysia 4-1.
The Indians put up an inspired performance and scored a goal in each half through V R Raghunath (6th minute) and Mandeep Singh (65th) to pick up their second win in the eight-nation event.
India, who need to win the tournament to qualify for next year's World Cup at The Hague, Netherlands, had thumped minnows Oman 8-0 in their tournament opener.
The Indians started brightly and dominated the early exchanges. In the first half India played possession hockey and utilised both the flanks to build up their attacks.
The Indians need to thank their goalkeeper Sreejesh as he made as many as six-seven clear saves to keep a clean slate for his team. He also earned the man-of-the-match award.
The Indians stunned Korea early in the match taking the lead through Raghunath. The well built defender converted India's first penalty corner with a powerful low dragflick to the right corner of the Korean goal past, beating goalkeeper Lee Myung Ho.
But thereafter, the Indians should consider themselves lucky not to have conceded a goal as Korea put the Indian defence under continuous pressure with repeated raids.
The Koreans earned as many five penalty corners in the opening half but failed to convert a single one.
While an onrushing Gurmail Singh blocked the Nam Hyun Woo's flick, an outstretched Sreejesh made one of his few brilliant saves from Korea's second short corner a few minutes later.
Five minutes from the break, India had a golden chance to double their lead but an unmarked Malak Singh shot wide from close range.
Towards the end of the opening half, the Indians unnecessarily invited pressure, conceding three more penalty corners.
But a brilliant Sreejesh under the goal once again came to India's rescue to deny the Koreans.
After the change of ends, the Koreans continued in the same vein and consistently put the Indian defence under pressure.
But Sreejesh stood like rock between Korea and goal as he made an acrobatic save in the 51st minute to deny Kang Moon Kweon.
If not for Sreejesh's efforts, India could have very well lost the match. The lanky custodian denied the Koreans on two to three occasions in the final 10 minutes to keep India afloat.
Towards the end, it was India's turn to exert some pressure on the Korean defence and came very close to doubling their lead, but an unmarked Malak shot wide with only the onrushing Korean goalkeeper Lee to beat.
But young Mandeep took the game away from Korea scoring India's second goal --- his fourth of the tournament - just five minutes from the hooter.
Mandeep slotted home with a powerful shot from top of the circle after snatching the ball from a Korean defender, who was unable to control Chinglensana Singh's cross.
India will play Bangladesh in their last pool match on Wednesday while Korea will be up against Oman.