The start of play was delayed by more than three hours on Friday, leaving 72 players unable to finish their round. There was another fog delay at The Belfry on Saturday and the third round will not be completed until Sunday.
Noren, a 26-year-old from Stockholm who played at Oklahoma State University, played four holes to complete his round. He started with a birdie on the sixth and parred the remaining three for a bogey-free round. He and Westwood were at 6-under 138.
Alejandro Canizares and Thongchai Jaidee both shot a 68 to sit a stroke behind the leaders, along with Marc Warren (71) and Ross Fisher (68).
Noren is seeking his first European Tour victory after finishing 20th at this years British Open, his first major.
That will be my goal, to play more majors, he said. Playing at that level and being up there for all four rounds, I could see what I need to do with my game.
On Friday, Westwood shot a 70 to take the lead and attempt to shake off a disappointing Ryder Cup performance by defending his title.
Graeme McDowell, the only other European Ryder Cup player in the field, shot an erratic 75 but made the halfway cut with a 3-over total.
Colin Montgomerie completed a 3-under 69 on Friday, but missed the cut because of an opening-round 81.