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 (69) was a shot behind the leaders.
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," he said.
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.
"I went out and played some solid stuff all day. I've done that for quite a long time," Bjorn said. "I have just got to try and keep focused, keep going with what I am doing. I am not making too many big mistakes out there and that is the key to playing this golf course."
Kaymer (67) kept pace for much of the day at Emirates Golf Club, holding a share of the lead after 11. But McIlroy birdied the 12th and Kaymer three-putted for a bogey on his 13th. Just when it looked like he might fall down the leaderboard, he made a hole-in-one on his 16th, hitting an 8-iron 180 yards.
"It was very similar to yesterday, hit a lot of good tee shots, a lot of fairways, a lot of good iron shots," Kaymer said. "I didn't make a lot of mistakes, so that creates a lot of birdie chances."
Westwood hit some of the best shots of the day. He closed with three birdies, including on the 16th where his approach shot rolled within a foot of the cup. At 18, his eagle chip skidded past the hole.
"I persevered really," Westwood said. "I gave myself a lot of chances out there and kept burning the hole. Just left a few putts hanging on the edges and I just had to be really patient and hit closer, and it was nice do that on 16 and 17."
The string of strong finishes sets up the prospect that three of the world's top golfers -- No. 1-ranked Luke Donald is not here -- will be competing for the title on Sunday.
That was not lost on Kaymer, who has twice beaten second-ranked McIlroy on the final day in Abu Dhabi.
"The only thing that matters is the trophy; to leave Sunday afternoon knowing you have beaten everyone. That is the pure satisfaction," Kaymer said. "A few players say the want to win, but they don't want it as much as others. Rory is one of those people. He really wants to win."
Despite two bogeys, Cabrera-Bello finished with two birdies over the last three holes for sole possession of third place.