Siddikur finished six under par to hold a one shot lead ahead of six other players - Thai pair Thongchai Jaidee and Prayad Marksaeng, Singapore's Lam Chih Bing, Filipino Antonio Lascuna and Koreans Park Hyun-bin and Hwang In-choon.
Westwood then leads five players two shots back, tied with Rory Hie, Ben Leong, Darren Beck and Mo Joong-kyung.
Should Luke Donald fail to win The Heritage in the United States this week, Westwood can overhaul Martin Kaymer at the top of the Official World Golf Ranking.
But first he will have to find a way to catch Siddikur, who looks to be on top form.
"I was hitting and putting very well and it has been like this for a few weeks now," said the Bangladeshi.
"I'm getting more confidence every week and that's why I've been playing so well."
Being paired with Westwood, however, means Siddikur has a constant reminder of his main challenge.
"I saw the draw yesterday and was feeling a bit excited playing with one of the best players in the world," he said. "I have to admit I felt a bit shaky this morning playing with Westwood."
Westwood had been struggling with his putting but closed with a pair of birdies.
"I played solidly but I was a bit frustrated out there," he said. "It has been the story for me so far, hitting it great from tee to green and giving myself a lot of chances but not taking it."
However, he insisted the ranking was not on his mind.
"I'll let things take their course and see what happens at the end of the week," he said. "Like I said before, I'm here to win a golf tournament."
Jaidee might have been the man in the lead had he not followed an impressive eagle with a double bogey after the turn.
"I was distracted by a camera and lost concentration from there on. I missed a lot of good putts on the back nine but made birdie on the last to put myself near the leader," he said.