Law covered the front nine at Al Hamra Golf Club in 33 before following an eagle on the 14th with three straight birdies on his way to recording a flawless second round of 64.
That gave the 31-year-old a total of 11 under par which was matched by Poland's Adrian Meronk and Denmark's Rasmus Hojgaard, the twin brother of defending champion Nicolai.
Law, who also shot 64 at the same stage last year to lead by two shots before finishing seventh, told Sky Sports: "It's really pleasing.
"I just stayed patient. I played good stuff the first 12 holes and didn't really hole too much, then the last six holes I putted really well which made a big difference.
"I'm excited (for the weekend). It's a different golf course than we've played the last few times we've been here.
"The fairways are that tight and firm that everyone's missing fairways so it probably does play into the hands of the bigger hitters a little bit, but at the same time there's quite a bit of skill involved in controlling your ball from the rough as well."
Hojgaard felt his opening 66 had looked better on the scorecard than it did on the course and was similarly unimpressed by a second round of 67.
"(It was) pretty much the same," the 21-year-old said. "I didn't drive the ball very good, put myself in the rough and the sand all the time but managed to putt well today and saved some good pars out there.
"It's one of the areas I want to improve and it's nice to see some of the stuff I've done paying off."
Asked about the prospect of succeeding Nicolai as champion and becoming the first brothers to win the same DP World Tour event, he added: "There's still quite a lot of golf left to play but it would be cool to make some history."
The round of the day came from England's Dale Whitnell, who carded nine birdies in a flawless 63 to lie a shot off the lead alongside compatriot Daniel Gavins, overnight leader Ryo Hisatsune and Wil Besseling.
"I didn't play very well yesterday (Thursday), it was a bit of a grind so very satisfying to shoot one under and then today I played a lot better," Whitnell said.
"I seem to be playing the hard holes really well and the easy holes not so well - I'm two over for the par fives - but I'm looking forward to the weekend."