Brier, who was two shots behind the South African after the first round, shot four birdies over his first nine holes on Friday to go five under and match the south African on a much calmer day after strong winds on Thursday had caused much havoc on the desert course.
Goosen, who also has nine holes to play in his second round, too had a bogey-free front nine, picking up birdies on the first and eighth.
A bunch of four players are a shot behind Goosen and Brier on four under. They include three former champions in Paul Lawrie of Scotland, Darren Fichardt of South Africa and Robert Karlsson, who won the title last year.
The only non-winner among them is South Africa's Thomas Aiken, although he has completed his round and is sure to slip down by the time Karlsson, Fichardt and Goosen are through for the day.
Meanwhile Martin Kaymer shot a 70 on Friday for an aggregate of three over par 147. Kaymer, who is challenging Lee Westwood for the world's top ranking, had a "birdie free" 77 on Thursday, but retrieved his position somewhat with a bogey-free second round.
"To be honest, I really struggled here," said the Kaymer who is hoping to become the first German world No 1 after Bernhard Langer. "I don't know why. I play good golf but I can't score."
Kaymer is almost certain to make the cut now and is contemplating making a charge for the title over the next two rounds.
"The thing is that the tournament here is very tight and no one is running away, and I am only seven shots off the pace. And I heard the weather is going to be good tomorrow, so i will play more aggressive in order to make a few more birdies.
"We'll see if I have a chance on Sunday."