Jeev and Randhawa shot three birdies each in a strong opening day performance. The lone bogey in the card came off Jeev's club on the par-three second hole.
Both the players opened with par shots on the first hole and after Jeev had stumbled to a bogey on the second, Randhawa made up for it with a birdie on the third hole.
Jeev himself found a birdie on the seventh hole as the Indians combined for one-under at the end of the front-nine.
The duo had a blemish-free backward journey and shared four birdies between them to round off creditable show on the opening day of the $5.5 million event's 55th edition.
The Irish team of Graeme Mcdowell and Rory McIlroy set the green ablaze with a 14-under 58 in the opening round to take a three-stroke lead.
The duo combined for 12 birdies and an eagle to be comfortably ahead of the chasing pack in which Argentina's Tano Goya and Rafael Echenique were the second spot with an 11-under 61. Defending champion Sweden was tied with Italy, Canada and South Korea six strokes off the lead at the Mission Hills Golf Club.
Thursday's round was played in alternate-shot format the first player tees off, the second player hits the second shot, followed by a shot from the first player, and so on until the ball is holed. Tee balls are alternated so that the same player doesn't hit every drive.
The second round on Friday will also be alternate-shot, so will be the final round on Sunday.
But Saturday's round will be played in the better-ball format in which each player on the team plays with his own ball until completing the hole. The lower of the two scores is recorded as the team score for that hole.
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