He had been joined in second place by Swede Joel Sjöholm, who was five under through eight holes.
Price has not finished among The European Tour's top 100 money-winners since 2004, and is chasing his first victory for nine years.
Helped by holing a bunker shot on the short 16th, his seventh, Price took over at the top from McGrane, although it was 5.30pm before the Irishman teed off again on seven under.
More than half the field will have to complete their rounds tomorrow morning, but unlike last month's Qatar Masters, which also had to be halted because of wind, it is still hoped to keep the event at 72 holes.
Sjöholm birdied the fourth to take solo second on eight under, with McGrane joined by José Manuel Lara,the Spaniard five under for the day with five to play.
South African Garth Mulroy matched McGrane’s opening 65, but coming after an opening 73 it left him tied for fifth on six under.