Brian Davis matched McGinley's 69 to move into third place at 11-under-par 205. Paul Casey and Simon Dyson each carded rounds of 2-under 70 to move into a tie for fourth at minus-9. They are joined there by first-round leader Bradley Dredge, who shot an even-par 72.
Tiger Woods seemed to battle his swing throughout the round, but still managed a 3-under 69. He shares seventh place at 8-under-par 208.
After a pair of fog delays the first two days, 78 players finished their second rounds Saturday morning. Among the leaders, Dredge saw the most action Saturday as he played 27 holes.
O'Meara started the third round at Emirates Golf Club one shot behind McGinley. Neither player made a move early as they each posted pars over the first six holes.
The duo finally got on the board with back-to-back birdies from the seventh. At the seventh O'Meara chipped in for birdie to briefly tie McGinley for the lead, but McGinley responded by sinking a 15-footer for birdie to reclaim the top spot.
At the next, O'Meara again birdied to tie the Irishman, but McGinley kicked in a three-footer to stay on top. Both men parred the next three holes around the turn.
O'Meara stumbled to a bogey at the 12th to fall two shots back after a poor tee shot. McGinley, meanwhile, continued to run off pars to stay in front.
O'Meara, who last won in 1998 when he titled at both The Masters and the British Open, began to make his move at the 14th after his approach shot hit the flag stick and stopped within 10 feet of the hole. He rolled in that birdie to get back within one shot of McGinley.
The American then drained a birdie putt from over 30 feet out at the 15th to grab a share of the lead. McGinley was unable to match O'Meara as his birdie try slid past the cup.
O'Meara then grabbed first place by himself at the 16th. He dropped his second shot within four feet and kicked in the birdie putt.
As darkness quickly fell over the course, O'Meara and McGinley with Dredge, their playing partner, rushed to complete the round. As the group ahead of them played out the par-5 18th, O'Meara and McGinley laid up with their second shots.
O'Meara knocked his third within 12 feet before McGinley knocked his third just over the back edge of the green. McGinley returned the favor to O'Meara as he chipped in for birdie and the tie. O'Meara left his birdie try hanging on the edge of the cup as the two men ended side-by-side atop the leaderboard.
'I can't focus on Tiger Woods. Certainly I wouldn't put it past him to come out and make a run tomorrow,' said the 47-year-old O'Meara. 'My concern, really, is to worry about myself. I'm not afraid of Tiger Woods, but I know what he's capable of. I think he's going to have to shoot pretty low tomorrow because I know Paul is playing well and there are other fine players, like Brian Davis, playing well too.'
'Nobody is ruled out of the equation. It's not just me and Mark,' McGinley stated. 'Anybody from six, seven, eight shots back can win if the wind blows because the course is playing that difficult. The course changed completely today. I seemed to be hitting away from the pins all day and if we get some wind tomorrow anybody could win from a long way back.
Woods got his round going with an up-and-down birdie at the par-5 third. At the fifth, he missed the green right and was unable to save par. He closed his front nine by rolling in an extremely long birdie putt on No. 8.
Around the turn, Woods continued to show his frustration. Several times he threw clubs after hitting his second shot, despite a couple of those shots finding the green. He two-putted for birdie at the par-5 13th and closed his round with an eight-foot birdie putt on the 16th.
'I played alright, but I didn't hit the ball all that close to the holes,' said Woods. 'Basically, the only putt I missed all day was on the 18th, but overall it was a pretty good day. Anyone on that leaderboard over there can definitely do it tomorrow.'
Woods is joined at minus-8 by Joakim Haeggman (68), David Howell (70) and Greg Owen (72). Thongchai Jaidee, Peter Lawrie, Jean Van de Velde and Lee Westwood are one stroke further back at 7-under-par 209.