Fulke shot a 2-under 70 on Friday, while Karlsson carded a 5-under 67. The duo is knotted at 8-under-par 136 at Doha Golf Club. Thailand's Thaworn Wiratchant fashioned a round of 4-under 68 and is alone in fourth place at minus-7.
Ernie Els, who won last week's Dubai Desert Classic, rebounded from his 1-over 73 on Thursday. In the second round, the third-ranked golfer in the world shot a 3-under 69 and finished 36 holes at 2-under-par 142.
Els has certainly had trouble in his first visit to Doha Golf Club.
'I can't really put my finger on it here,' said Els. 'A lot of times, you hit what you think is a good shot and it finishes nowhere. I hit a lot of good shots, but the ball scatters away from the hole. At least I played better.'
Els will be gunning for Green on the weekend.
Green, a lefthander who lost to eventual winner David Toms in the first round of the WGC-Accenture Match Play Championship, tallied a pair of birdies at his first two holes.
He stumbled on the front nine with back-to-back bogeys from the fifth, but climbed up the leaderboard with his outstanding play early on his second nine.
Green birdied three holes in a row from the 10th to reach 8 under par and tie Fulke for the lead. Green got one clear at the 16th as he collected his second birdie in as many rounds, then parred the final two holes for his first 36-hole lead on the European Tour since last year's KLM Open, where he tied for second place behind David Lynn.
The 34-year-old Green has only one win on tour, the 1997 Dubai Desert Classic, and would love to win both European Tour stops in the Middle East.
'It would be awesome, but there is a long way to go,' admitted Green, who knows that Els is seven back. 'You can never write him off. He's No. 3 in the world and renowned for shooting low scores. I wouldn't mind betting he puts together a 6 under round or something like that. '
Fulke, who played on the 2002 Ryder Cup team, birdied his first hole, then dropped shots at two of his last three holes on the front nine. He mixed four birdies and one bogey on the back nine for his 70.
Karlsson, who shares the course record of 63 at Doha Golf Club, got nothing going on his front nine. He holed out a bunker shot for par at the eighth, but he vaulted up the board from there.
After birdies at the ninth and 10th holes, he then chipped in again, this time for birdie at the par-4 12th. Karlsson finished with birdies at 16 and 17 to get within one of the lead.
'I struggled a bit on the front nine, but got it together on the back nine,' said Karlsson.
Gregory Havret (67), Raphael Jacquelin (68) and David Park (70) are knotted in fifth place at 6-under-par 138. Arjun Atwal (69), Niclas Fasth (71) and Ricardo Gonzalez (70) are tied for eighth place at minus-5.
The 36-hole cut fell at 1-over-par 145 and Joakim Haeggman will not be able to successfully defend his title. He shot a 3-over 75 on Friday and missed the cut by one stroke.