Willett shot 3-under 69 for the day for a 54-hole score of 12-under par 204. He carded six birdies that offset a trio of bogeys, including one on the 18th hole.
"The wind was whipping around a bit, but I drove the ball great which makes it a lot easier around this golf course," Willett said. "If you want to be in contention, you have to have things go your way a little bit."
Willett is seeking his first European Tour victory.
Sjoholm, the second-round leader, came in at even par 72 for the day as did Wood.