Paul Dunne is four under par, three shots off the leading group of six golfers.
Starting at the 10th hole, Molinari registered a hat trick of birdies from the 14th which he capped by draining a brilliant 20-footer at the 16th.
Marcus Fraser was understandably thrilled after claiming a share of the second-round lead at the Italian Open with a stunning round of 62. He finished his front nine in style, chipping in for a birdie at the 18th to get to five under before picking up further shots at the first and second.
"To come and do that today, I'm pretty proud of myself and it's quite reassuring that I still can play golf", said Fraser, a three-time European Tour victor ranked a dismal 136th in the Race to Dubai.
Fraser, who put together a streak of five successive birdies between holes eight and 12, told EuropeanTour.com: "I felt like I've putted well and scrambled well this week".
"I just played good golf out there today and it's flawless weather for us to shoot low", Wallace said.
Having entered the Rolex Series, the tournament features an increased purse of US$7 million this year as part of the buildup to the 2022 Ryder Cup outside Rome.
Padraig Harrington is back on two over.