The duo finished 36 holes at 13-under-par 131 and share a one-stroke lead. McIlroy won twice last season, including his first major championship title as he claimed the U.S. Open, while Bjorn picked up three victories last season.
First-round leader Rafael Cabrera-Bello posted a three-under 69 and is alone in third place at minus-12.
Martin Kaymer, the world No. 4, shot five-under 67 in round two. He shares fourth place at 11-under 133 with Gregory Bourdy (67) and Scott Jamieson (68).
There have been good scoring conditions through two days as 81 of the 138 players that started the week were under par after two rounds on the Majlis course at Emirates Golf Club.
McIlroy, who was the youngest ever winner of this event when he won in 2009, was in the morning wave and started on the 10th tee. He birdied that hole for the second straight day, then also birdied the par-five 13th for the second round in a row to move to minus-eight.
The 22-year-old Ulsterman converted a birdie try on the 17th and made it two in a row with a two-putt birdie on No. 18.
Around the turn, he wrapped pars on four of the first five holes around a two- putt birdie at the par-five third. That gave McIlroy birdies on all four par- fives in round two, and he has played those holes at minus-seven through two rounds.
McIlroy rolled in a five-foot birdie putt on the sixth to move three clear of the field at minus-12 and got into the clubhouse first at 13-under after he birdied the par-four eighth.
"I just kept picking up birdies along the way and it puts me in a great position. I feel a lot more confident than I did in Abu Dhabi," McIlroy admitted. "I played very, very well today."
Bjorn, who played in the afternoon wave, had one birdie and seven pars through eight holes. He caught fire starting at the ninth.
The Dane converted a short birdie chance at nine and followed with birdies on 10 and 11 to jump to 10-under. He got within two of the lead thanks to a birdie on the 13th.
Bjorn, the 2001 champion, parred three straight before making birdie on both 17 and 18 to join McIlroy atop the leaderboard.
"I played quite well on the front nine, but didn't really hole any putts. They came on eight, nine and 10, where I made birdies there," Bjorn said. "I finished it off in good style. This good round came off the back of other good rounds."
World No. 3 Lee Westwood also fired a 65 to move into a share of seventh place at 10-under-par 134. He was joined there by Stephen Gallacher (65) and Marcel Siem (69).
NOTES: Kaymer had a hole-in-one on No. 7 for the second ace of the week...Defending champion Alvaro Quiros carded his second straight 70 and is tied for 27th at minus-four...The cut line fell at one-under-par 143 with 81 players moving on to the weekend...Americans John Daly, 1995 winner Fred Couples and 2004 champion Mark O'Meara all made the cut on the number...Among those that missed the cut were former champions Robert-Jan Derksen, Jose Maria Olazabal and Richard Green, as well as Anders Hansen, Michael Campbell, Peter Uihlein and Shaun Micheel.