Rock closed with five consecutive birdies while Wood was 8-under for his last 10 holes.
They are one stroke ahead of Rafael Cabrera-Bello, Thorbjorn Olesen and Scott Jamieson with another seven players tied at 5-under. A total of 92 golfers beat par on Turin's Royal Park I Roveri course.
Wood and Rock, who are paired together for at least the first two rounds, played the back nine first Thursday. Wood opened with seven pars but had a birdie at No. 18. He posted four birdies over Nos. 1-5.
He finished with a 12-foot putt for eagle at the par-5, 547-yard eighth hole and a 5-footer for birdie at the ninth.
Rock opened with back-to-back birdies. He added another at No. 15 but gave that back with a bogey at the 16th. After a birdie at No. 2 he closed with a flourish, getting birdies on each hole from 5-9.
"It was good playing with Rocky and we seemed to fire off each other," said Wood. "It was a good round without a bogey, always nice to play that way."