Rock stood at 12 under midway through the tournament at the Royal Park Roveri club.
Rock’s fellow Englishman Chris Wood and Joost Luiten of the Netherlands were tied for second at 11 under, with six players – including Italian favorites Matteo Manassero and Francesco Molinari – tied at 10 under.
Rock has finished runner-up three times on the European Tour.
“I hope I can keep this feel for the next couple of days here and take that into the U.S. Open next week,” Rock said following a round that was interrupted by a rain delay.
With most of the top players preparing for next week’s major at Congressional Country Club in Bethesda, Md., this event features only two players in the top 50 of the rankings – Manassero and Molinari.
The round of the day belonged to Victor Dubuisson of France, who shot a 10-under 62 to lie in an eight-way tie for 10th at 9 under. Dubuisson’s memorable round featured 10 birdies.