McDowell , a three-time European Tour winner, shot a 5-under 66 and Khan fired a 68 for a two-shot advantage.
Ross Fisher (68), Jeeve Milkha Singh (69) and Richard Green (70) tied for third at 205.
Six players were another two strokes back, including Adam Scott and Ian Poulter, who both shot 68.
Former U.S. Open champion Angel Cabrera, who led at the halfway mark, slipped to a 7-over 78 and fell to a tie for 37th place.
"I went out there with 3- or 4-under-par in mind," the 28-year-old McDowell said. "I thought that would make a good impact on the leaderboard. Obviously, it was really nice to shoot 5under."
Khan, 36, has one victory on the tour.
"When I've been in good position, I've tried a little bit too hard," he said. "And sometimes you can just push it away when you want (to win) too bad." But, he said, "I feel confident."