Stenson, the 2007 champion, finished two rounds at 11-under 133 and is one ahead of Richard Green, who posted a 9-under 63 on Friday at Emirates Golf Club.
For the second consecutive day, there was a significant fog delay that prevented the start of play on time. The first round was completed on Friday morning, but with another significant delay, some players did not even get the chance to tee off in round two.
The golfers will return to the course on Saturday morning and polish off the second round. The halfway cut will occur and then the plan will be to play as much of the third round as possible.
'It was a grinding day,' acknowledged Stenson, who was a joint runner-up last week at the Qatar Masters.
World No. 2 Sergio Garcia carded a 6-under 66 and is alone in third place at minus-8.
First-round leader Rory McIlroy is 1 over through three holes and is at 7 under par.
Stenson began on the 10th tee Friday and birdied the par-5 10th for the second time in as many rounds. He birdied the par-3 15th and closed his opening nine with a birdie at the par-5 18th, a hole he bogeyed in round one.
Stenson cruised on his second nine. He birdied one, four, seven and nine to move one clear of Green.
'When I hit bad shots I recovered well and made some good birdies on the good shots so it was a very well-scored round,' said Stenson, who is ranked seventh in the world. 'I made some nice putts and kept it together nicely.'
Since so many players still need to finish the second round, and with Stenson expected to be at least near the top the of leaderboard once that round is finalized, he will have quite a long wait until his tee time on Saturday.
How does Stenson intend to use the time?
'Sleeping,' stated Stenson. 'I'm very happy to have finished. To have to go out tomorrow and have to hang around in a possible fog delay and maybe play one hole, that's going to be a real pain.'
Newly minted European Ryder Cup captain Colin Montgomerie posted his second consecutive 2-under 70 and is part of a group tied for 13th at 4-under 140.