Englishman Rock held a share of the overnight lead with compatriot Chris Wood and a round of 68 moved him to 12 under for the tournament, held at Royal Park I Roveri near Turin.
Rock had just a single bogey on his card, at the par-3 15th, but picked up five birdies including a four on the final hole which took him to the top of the leaderboard.
"I putted really well yesterday but today I hit a few that came up short of the hole," said the 34-year-old, after a day when almost an hour-and-half of play was wiped out due to poor weather. If I am watching it from halfway it's usually pretty good. I hope I can keep this feel for the next couple of days here and take that into the US Open next week - that would be great. I'm excited about playing the US Open. My long game can handle it, but can my putting stand up to it as well?
"All I can do is work hard and keep practising and hope that a win will eventually happen. Some people manage it straight away and some take a bit of time and I've passed 200 tournaments now. I hadn't attempted to qualify for the US Open before so it's going to be a great experience going to Congressional next week."
Compatriot Wood remains close behind, though, just one shot back on 11 under after a second round of 69 which included five birdies and two bogeys.
Wood, who partnered Rock and Marcus Fraser - who enjoyed a hole-in-one at the fourth on the way to a 66 - said: "The three of us did well. I think between us we are 30 under par and Marcus had a hole in one and almost a second. That doesn't do any harm as you can feed of what other players are doing. It can definitely spark you into doing something."
Wood was joined in a share for second spot at the halfway stage by Dutchman Joost Luiten, who climbed the standings with a five-under 67 round. Luiten sank five birdies and added an eagle on the par-5 11th to boost his score.
Italian duo Francesco Molinari and Matteo Manassero sat among a group of six players tied for fourth - two shots behind Rock.
Delighting the home galleries, Molinari recovered from an early bogey to sink five birdies on his way to a round of 68, while teenager Manassero also recorded five birdies, with a dropped shot on the 15th his only blemish.
"It's very nice to be back home and seeing friends," said Molinari. "I had a few busy days but now the focus is totally on the golf. I know the course inside out, but I was saying yesterday sometimes that is an advantage and sometimes not. You have memories of the course, some good and some bad, and you have to draw on memories of shots you might have hit ten years ago."England's Gary Boyd joined the Italian duo with a fine seven-under 65 yesterday which saw him leap 27 places, with Welshman Rhys Davies, Frenchman Gregory Bourdy and another Italian, Lorenzo Gagli, completing the group.
Davies, who impressed with his putting, said: "I did a lot of putting when I was younger and I guess I grew up on fairly fast links greens which may have helped and putting in the wind you need a good rhythm so maybe that has something to do with my putting stroke."
Gagli was another big mover yesterday climbing 16 places with his round of 66, while Davies carded five birdies and one bogey to complete the second round in four under.
Northern Ireland's Darren Clarke saw a major improvement on his opening round of 71 by picking up six shots to finish the day on seven under overall.
Defending champion Fredrik Andersson Hed sits two shots further back after a three-under 69, but Colin Montgomerie missed the cut despite a better performance in the second round.
The Scot signed for a three-over 75 on Thursday and although he carded a two-under 70 yesterday, it was not enough to take him through to the weekend's play with the cut projected at 141.
How Montgomerie would have loved to swap places with young Frenchman Victor Dubuisson.
The Nice-born 21-year-old had a terrific ten-birdie 62 to make amends for his opening 73 and surge to nine-under, just three behind Rock.
While Montgomerie headed out of the tournament, eight Scots survived the cut to take part in the weekend's action. They were headed by Peter Whiteford, who added an excellent five-under 67 to his opening 68 to lie in a share of tenth spot on nine-under. Richie Ramsay is a shot behind, with Lloyd Saltman now six under par, David Drysdale and George Murray five under along with Jamieson, and Gary Orr and Alastair Forsyth on four-under. As well as Monty, Jack Doherty, Marc Warren and Elliot Saltman also missed the cut, while Steven O'Hara withdrew following his opening six-over round of 78.