Richard Green and Jamie Donaldson joined the South African atop the leaderboard at the Majlis Course at Emirates Golf Club. David Lynn and Ross Bain are tied for fourth place at minus-6.
Woods wasted little time in breaking into red figures as he birdied the second hole. He eagled No. 3 and birdied No. 4 to reach 4 under par through four holes.
The No. 1 player in the world cooled a bit as he parred his final five holes on the front nine. He bogeyed the 10th, but rebounded with a pair of birdies in a three-hole span early on the back nine.
That would be all for the reigning Masters champion and British Open winner.
Goosen, who played only two rounds in the last six weeks, opened on the back nine and struggled off the tee. He went way left at 10, but saved par. It was right off 11 and left off 12, but both times he was able to get up and down.
At the par-5 13th, Goosen hit a 5-iron with his second shot and knocked it to 20 feet. The South African converted the eagle putt, then closed his first nine with three straight birdies from the 16th.
Goosen, who won the South African Airway Open at the end of last year, kept the strong play going on the second nine. He birdied the first for four in a row, then birdied the par-5 third hole and parred his next five before reaching 8 under with a birdie at the ninth.
'It was nice to get off to that start and then I had a good run in the middle of the course,' said Goosen, who has not played in this tournament since 2001. 'I must say coming out, I didn't expect a lot. I missed a lot of fairways, but I made a lot of putts.'
Green, who won this tournament in a playoff against Ian Woosnam and Greg Norman in 1997 with his wife on the bag, birdied two and three, then collected his last birdie of the front nine at the par-4 ninth.
On the second nine, Green caught fire. He recorded birdies at four of his first five holes, including three in a row from the 10th. The Australian polished off his 64 with a birdie at the 17th.
Throughout his practice rounds all week, the memories of his 1997 victory have loomed large. That has been his only win on the European Tour, despite three straight top-55 finishes on the Order of Merit, and the Australian might be ready to return to the winner's circle.
'It's nice to go out and shoot a good score and bring back all of those memories of '97,' said Green. 'I kind of hope to play like these boys and make it happen, rather than get lucky. That's the way I see it now.'
Donaldson, who has been crippled by back problems in recent years, parred his first four holes, before tallying his first birdie at the fifth. That was his only birdie on the first side and Donaldson did not fly out of the gate on the back nine. He made only one birdie in his first three holes, but fortunes changed at the par-5 13th.
Donaldson birdied that hole, then ran the table to finish with six consecutive birdies. Donaldson could not recall a birdie streak of more than five, but the Welshman has a simple strategy.
'I just concentrate on staying out of my own way and letting things happen,' said Donaldson. 'I wasn't really aware of how many I had. I knew I had quite a few and was quite surprised to see six in a row when I got in.'
Last week's Qatar Masters champion Henrik Stenson, Paul Casey, Nick Dougherty, Niclas Fasth and Nick O'Hern joined Woods in sixth place at minus-5.
Defending champion and three-time winner Ernie Els carded a 4-under 68 on Thursday. Darren Clarke, Costantino Rocca, Lee Westwood and Barry Lane are among those who are tied with Els in 12th place.