After thunderstorms ended play prematurely on Friday, Poulter completed the remaining four holes of his second round in one under.
That gave him a six-under round of 66 and a halfway total of 14-under-par.
Veteran Spaniard Miguel Angel Jimenez parred the four holes he had to finish, adding a 73 to his opening 63, to leave him in a six-way share of second place.
Poulter, who birdied five of the first 11 holes on Friday, tweeted that evening: "Now that was a close call. On 14th green when lightning struck very close by."
After three-putting the 12th to drop a shot, the world number 40, aided by a strengthening wind, reached the par-five 13th green in two shots to set up a simple birdie.
And on Saturday he birdied his first hole of the day, the 15th, to boost his chances of a first European Tour victory in two years.
The 38-year-old is now 33-under-par for his last six rounds at the Colin Montgomerie-designed Maxx Royal course.
"I played exactly the same last week but didn't hole my putts," said Poulter, who finished joint sixth in the WGC-HSBC Champions last Sunday, the tournament which provided his last win in 2012.
Ryder Cup player Victor Dubuisson, who won the inaugural tournament last year, was 13 shots off the pace and one over.
The Frenchman, who played with a persistent nose bleed in round two on Friday, birdied the last for a round of 68.
World number four Sergio Garcia, the highest ranked player in the field, is two over after recording triple bogey sevens at different holes in both of his opening rounds.
The tournament is the third event of the European Tour's Race to Dubai Final Series, which culminates with the World Tour Championship in Dubai from 20 to 23 November.
Ian Poulter extended his lead to six shots after round two of the delayed Turkish Airlines Open in Belek.