Stenson made five consecutive birdies from the 13th hole, using his putter only three times.
"I was just hoping to go out there and shoot under par like I did yesterday (70) and hopefully move up the leader board," said Stenson. "I certainly did that, and I'm now in a nice spot."
Westwood birdied on the 17th and 18th holes and finished with a one-under-par 70.
Stenson now has a four-under-par score of 138, while Westwood is three-under-par at 139.
The Volvo Masters is the final event on the European Tour.