Those late birdies moved Els two clear of the field at 17-under-par 199. Second-round leader Ross Fisher managed a 71 and shares second place at minus-15 with Henrik Stenson (69) and Jyoti Randhawa (67).
The second and third rounds at Emirates Golf Club were both completed Saturday morning. The second round was suspended Friday night due to darkness after weather delayed action for over two hours Friday afternoon.
Woods trailed by as many as six strokes early in the round before a birdie on the fifth moved him to minus-10. He dropped a shot on eight, but atoned for that error with a birdie on nine.
The 31-year-old came right back with birdies on 10 and 11 to move within two strokes of the lead at 12 under. Woods parred his next five holes before closing with birdies on 17 and 18 to finish three behind Els.
'When you are chasing and coming from behind you can't afford to make mistakes,' Woods explained. 'That's the great thing about leading, you can slip up and still win the tournament. But coming from behind and given the golf course we have here, you have to make a bunch of birdies. I have to try and do that and hope it is enough.'
Els, who won here in 1994, 2002 and 2005, entered round three one behind Fisher. Els faltered to a three-putt bogey on the first. He erased that mistake with a birdie on two.
The South African birdied the third as well, but remained one back as Fisher also birdied the third. Fisher stumbled to a bogey at six to fall back into a tie for the top spot with Els and Stenson.
Els bogeyed the eighth to again fall one down. He got that stroke back with a birdie on 10. After Fisher bogeyed 11, Els took the lead with a birdie on 12. Fisher and Stenson birdied the 13th to forge another three-way tie for the lead.
After four straight pars, Els converted a 3-foot birdie try on the par-4 17th. He made it two straight as he two-putted for birdie on the 18th to finish two clear.
'It is a great golf course and it will produce a good test (Sunday) that is for sure,' Els stated. 'We have a great leaderboard and the number one player in the world is in there too, so it is going to be great. But it is important to play your own game and concentrate on what you have to do. I have a good game plan.'
Fisher was even par through nine with a birdie and a bogey. After a birdie on 10, he dropped a shot at 11. Fisher's final birdie came at 13 before he parred out to share second.
Stenson connected on consecutive birdies from the second. However, he turned in even par after bogeys on seven and nine. Stenson fought back into the mix with birdies on 10 and 11.
He made birdie on the par-5 13th for the third straight round to move to 15 under, before closing with five pars.
'It is pretty bunched up and a lot of guys will have a chance (Sunday), but the good thing is that I'm one of them,' Stenson said. 'Obviously Woods is in there, but Ernie is playing very well and I think he is going to be the one to look out for.'
Randhawa used a strong back nine to move into contention. He had a birdie and a bogey through nine holes. The 34-year-old moved to 12-under with birdies on the 10th and 13th. He closed with three straight birdies to grab a share of second.
Niclas Fasth flew up the leaderboard in round three with the low round of the day, a 7-under 65. That moved him into a share of sixth with Peter Hanson at 13-under-par 203. Prom Meesawat in one stroke further back at minus-12 after a Saturday 68.
Thomas Bjorn (66), Simon Dyson (69), Joakim Haeggman (69) and Robert Karlsson (68) are tied for ninth at 11-under-par 205.