Rock turned in a 4-under-par 68 in the second round and is at 12-under 132 after 36 holes. He's one stroke up on Joost Luiten and Chris Wood.
Luiten had four birdies, an eagle and a bogey in a six-hole stretch en route to a 5-under 67. Wood, who shared the first-round lead with Rock, had five birdies and two bogeys for a 69.
Six players are tied for fourth at 10-under, with another eight at 9-under 135. That group includes Victor Dubuisson, who fired a bogey-free 10-under 62.
After a par at the first hole, Rock pulled into the lead alone with birdies at Nos. 2 and 3. Back-to-back birdies at 11 and 12 got him to 4-under but he fell back with a bogey at the 217-yard, par-3 15th hole. A birdie at 18 gave him the outright lead.
Celebrity Families of 2014 [PHOTOS]