Randhawa, with a total of eight-under 208, will enter the final round six shots behind leader Phil Mickelson (67), who is chasing his fourth title of the year.
Randhawa acknowledged that he would need a special effort on Sunday to upstage Mickelson and world number one Tiger Woods (70), who is tied for the second spot at 12-under.
"It's not easy out there. Guys are trying to get aggressive and they make a few bogeys and suddenly you're out of the tournament," he said.
"So I just played consistent golf, stuck to what I needed to do and made some putts," conceded the 2002 Asian Tour number one.
After opening with a couple of pars, the Delhi-pro stumbled to a bogey on the third hole before hitting back-to-back birdies on the fourth and fifth.
But a dropped shot on the sixth brought him back to square one before a birdie on the ninth hole helped him make the turn one-under.
His back-nine was a subdued affair and Randhawa found a birdie on the 16th hole for the second successive day to round off a steady day.
Among other Indians, Jeev Milkha Singh also carded a 70 to rise 13 places to tied 32nd with an overall total of one-under.
Further down, C Muniyappa (78) and Gaganjeet Bhullar (76) continued to struggle and were tied for the 60th and 71st place respectively.
While Muniyappa has a total of five-over, Bhullar is 10-over overall.