Thongchai shot a 69 to keep a share of the lead, and was also joined by Alvaro Quiros (67) in a quartet with 11-under totals of 205.
Despite being joined by some of golf's biggest names atop the leaderboard, Thongchai said he liked his chances ahead of Sunday's final round.
"I am confident I can win here," the 41-year-old former Thai army paratrooper said. "In today's round, I did not hit many greens over the first nine holes, only four in regulation, but I only had 10 putts. If I hit more fairways and greens in the final round then I will score better, and I know I am capable of that."
Westwood is looking for another title in the desert, after winning the Dubai World Championship in November.
"If the weather stays calm as it did for the third round it's going to be a birdie feast," Westwood said.
Quiros said learned a lot when partnering the 60-year-old Tom Watson during the first two days.
"Tom is a very smart player," Quiros said. "He's is a very clever player and even at 60 years old that still makes him competitive. Playing with him, he made three very smart lay-ups instead of going for greens. But with my length, I find it very difficult not to go for everything even when I am in the rough. ... It's something I am having to learn."