Randhawa, three-under through two rounds, shot five-under 67 on the moving day to get to eight-under 208 and tied-ninth place.
SSP Chawrasia added a four-under 68 to his three-under 141 total for 36 holes and is now seven-under 209 in tied-14th place.
Among other Indians, Arjun Atwal and Shiv Kapur carded three-under 69 each in the third round to move to five-under 211 and in tied-22nd place, while Rashid Khan (70) and Gaganjeet Bhullar (72) are at three-under 213 and tied-34th place.
"I was pretty focused today. I guess that was the key to me playing well. I made six birdies and a bogey. It was great playing alongside Bubba (Watson). He's a very nice person. We've got a great crowd following us so it was really enjoyable out there," Randhawa said.
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"It was very hot out there but it got cooler on the back nine as the windy was up a little. My chipping wasn't good today. I wished I had chipped better and made some up and downs. I just got to improve my short game for tomorrow," he added.
Leader Sordet said, "It's pretty much my dream to play
with the top players in this field. I think I will do that tomorrow and hopefully I'll enjoy it and just play my own game,"
And then comes Westwood.
The Englishman is a master of the Amata Spring layout, having won in 2011 and 2014, and with an eight-under par 64 leaving him at 13-under, the trophy is well and truly in his sights once again.
The charge the packed galleries had hoped for from world number four Bubba Watson never materialised today. The American signed for an even-par 72 that left him on three under and shaking his head.
Still in the hunt also are rising South Korean star and freshly minted European Tour Rookie of the Year -- An Byeong-hun, who sits in fourth after a four-under 68 that left him at 12 under and four off the pace. While world number 12 Sergio Garcia and two-time major winner Martin Kaymer sit tied for fifth a further stroke back on 11-under after rounds of 70 and 72, respectively.