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Jeong Suk-Young gave the Koreans an unbeatable 3-1 lead by outplaying Virali-Murugesan Ranjeet 6-4, 6-4, 6-2 in the day's first match.
Nam Ji-Sung beat Vijayant Malik, the other Indian debutant, 6-2, 6-4 in the inconsequential fifth rubber that was reduced to best-of-three sets.
South Korea will now meet Japan in the second round in April, with the winner qualifying for the world group play-offs later in the year.
India play Indonesia, also in April, to remain in the regional group one.
India went into the tie with veteran Leander Paes as the only first-choice player after 11 team-mates refused to play following a dispute with the All India Tennis Association.
Somdev Devvarman, Mahesh Bhupathi and Rohan Bopanna were among the players who stayed away, leaving newcomers Ranjeet and Malik as the two singles players.
India's lone point in the tie had come through the doubles team of Paes and unheralded Purav Raja on Saturday.