Colin Montgomerie had rough round and missed the cut after shooting a 7-over 79 for a two-day total of 150. He had one double bogey and five bogeys.
It is the first time since last September's Lancome Trophy that he has missed a halfway cut.
Wi put together nine consecutive birdies during his round, but Els' eagle on the final hole of the day moved him to a shot of the lead. Wi has a two-day total of 9-under 135, while Els is at 136 after his second-round 68.
Els, who won here in 1994, overcame a bogey on the 14th hole with what he called one of the best shots of his career -- a 213-yard second shot from the sand to 35 feet. He then made the putt for eagle in the par-5 hole.
'That shot was one of the best if not the best of my career,' said Els, who won the Genuity Championship last week in Miami. 'I am looking forward to the rest of the tournament, but a lot of guys are in there who are under par who also have a chance.'
John Bickerton of England and Niclas Fasth of Sweden are tied for third with 7-under 137s.
'I can't afford to think too far ahead,' Wi said. 'I can only go out and play one shot at a time. I have to stay relaxed.'
Full field scores from the Dubai Desert Classic