JOIN USCompatriots C Muniyappa (69) rose to tied 37th at 143, two strokes ahead of Jeev Milkha Singh (72), who was tied 45th after the second round. Gaganjeet Bhullar (150) could not improve his position and followed up his opening round 74 with 76 to slip to tied 70th.
Randhawa, a 10th tee starter, was even-par at the turn and he sunk three birdies, against one bogey, in his front nine to sign off with his second successive sub-par card.
Muniyappa was one-over after his first six holes before he bounced back, firing four birdies over his next five holes to bring home the best card of the day by an Indian.
Tiger Woods birdied his final hole to complete a second round five-under-par 67 that moved him into a share of the lead with American compatriot Nick Watney at the halfway stage.
The world number one had spurned a raft of birdie chances early on another sunny day at the Sheshan International but made no mistake with a short putt at the 18th and joined first round leader Watney, who shot a 70, on 10-under for the tournament.
World number two Phil Mickelson picked up his sixth birdie at the last for a 66 to stand a stroke behind the leaders, alongside compatriot Ryan Moore (69) and Spain's Alvaro Quiros (66) in a share of third.