The pair is knotted at 11-under-par 133 at Doha Golf Club.
Australia's Nick O'Hern posted a 3-under 69 and is alone in third place at 9-under-par 135.
Defending champion Henrik Stenson carded his second consecutive round of 4-under 68 and is tied for fourth place with 1999 British Open champion Paul Lawrie (67), Wen-Chong Liang (67) and Spain's Miguel Angel Jimenez (70) at minus-8.
Goosen began on the back nine Friday and collected a pair of birdies in his first three holes. He added back-to-back birdies at 16 and 17 to make the turn at 4-under-par 32.
Goosen got to 12-under par for the championship with his second birdie at the par-four second in as many days. Unfortunately, Goosen dropped only his second shot of the tournament at the fifth to fall into a tie for the lead.
'I birdied the second hole, but then lost my concentration on the fifth and suddenly I wasn't making anything,' said Goosen. 'But there are 36 holes to be played and a lot can happen. I just need to get a good round in tomorrow and make a few putts.'
Green, an Australian, played Doha Golf Club from the first and tallied four birdies in his first six holes. That birdie run got him to 8 under par for the tournament, but his play on the second nine vaulted him to the top of the leaderboard.
He birdied the par-four 11th, then birdied Nos. 16 and 18, as he did on Thursday, to join Goosen in the lead.
'I played very nicely the first two days,' said Green, who is the only player in the field without a bogey this week. 'It has been quite a pleasure being out there playing golf. I have hit some really nice shots and never looked like making a bogey. It has been nice.'
The co-leaders have enjoyed wildly different European Tour careers.
Goosen, a two-time U.S. Open champion, has posted 13 wins on the European Tour and is currently ranked eighth in the world. Green has only one victory on the circuit - the 1997 Dubai Desert Classic - and came in 67th in this week's rankings.
'I would like to have another one,' admitted Green. 'It would be fantastic. I play well over here and always play well at this time of the year so I like to make the most of it.'
Edward Michaels (69), Chinarat Phadungsil (68) and Jeev Milkha Singh (68) are tied for eighth place at 7-under-par 137.
Several high-profile players are back in the mix, further down the leaderboard.
Stuart Appleby (69), Chris DiMarco (66) and former European Ryder Cupper Paul McGinley (68) are part of a group tied for 13th place at minus-5. Former major winners Michael Campbell (70) and Ernie Els (71) are part of a logjam in 20th at 4-under-par 140.
The 36-hole cut fell at even-par 144 with 75 players advancing to the weekend. Two prominent European Tour players missed the cut - last week's winner in Abu Dhabi, Paul Casey (145) and Darren Clarke (151).
The Golf Channel will have coverage of all four rounds beginning at 9:30 a.m. ET each day.