McIlroy made seven birdies, including a 25-yard chip-in on No. 8. He overtook first-round leader Rafael Cabrera-Bello with a 13-under total of 131.
“I was never really under pressure in any point of the round,” said McIlroy, the 2009 champion. “This was very stress-free golf; fairways most of the time, a lot of greens, and gave myself a lot of looks.”
Bjorn closed with two birdies to tie McIlroy, finishing with five birdies on the back nine. Cabrera-Bello, with 69, was a shot behind the leaders.
Fourth-ranked Martin Kaymer made a hole-in-one on 16 to trail by two strokes with 67. Third-ranked Lee Westwood birdied his last three holes to reach a 10-under 65.
McIlroy liked his improved driving after inconsistencies led to a second-place finish at the Abu Dhabi Championship two weeks ago.
“I’ve put that right for the most part and felt really confident off the tee,” said McIlroy.
Bjorn, who beat Tiger Woods to win the tournament in 2001, started his charge on the ninth when he made three straight birdies and closed with another pair for a bogey-free 65.
LADIES EUROPEAN TOUR: In Melbourne, Australia, U.S. Women's Open champion So Yeon Ryu shot a 4-under 69 to take a one-stroke lead over fellow South Korean player Hee Kyung Seo in the Women's Australian Open.
Ryu, a playoff winner over Hee in July at the Broadmoor in Colorado Springs, Colo., had a 6-under 140 total on Royal Melbourne’s Composite Course, the 2011 Presidents Cup venue that is hosting a women’s professional event for the first time.
“Today, my plan was always just par,” Ryu said.
Seo shot a 66, the best score in the first two days of the tournament. She had nine birdies and two bogeys.