Rain and murky conditions could not prevent Molinari breaking the record by a shot to lie one stroke ahead of Swede Johan Edfors.
While Molinari and Edfors excelled over the Baltray links, it proved a poor afternoon for three-times major champion Padraig Harrington. Harrington is 10 shots off the lead and is also six strokes behind his compatriot, amateur Shane Lowry, the leading Irish player.
"Every time I think I'm moving forward I end up moving backward, it's kind of like that at the moment," Harrington, who on Wednesday said he was adjusting his swing, told reporters.
"I just have to stay patient and work through these things."
Molinari, whose sole European Tour win came in the 2006 Italian Open, was untroubled by the bad weather.
The 26-year-old, already with a second, two third places and a sixth place this season, said he had developed a new confidence in his short game.
He has taken on European Ryder Cup captain Colin Montgomerie's coach, Denis Pugh, to strengthen this part of his game.
"The worst part of my game used to be my short game and now it is so much better. I think I am playing better than when I won the Italian Open," the leader told reporters after handing in a card containing an eagle and eight birdies.
Edfors found the form that earned him three European Tour titles in 2006, gleaning 10 birdies.
The Swede revealed an Irish connection that has benefited him this week.
"One of my sponsors is an Irish pub called the Dubliner," Edfors told reporters.
"The owner was the only one to help me out when I was struggling on the Challenge Tour. It means I come over and play a lot of courses like this week, so I'm used to links."
Montgomerie and 20-year-old Northern Irishman Rory McIlroy played together, with the younger man outdoing his potential Ryder Cup captain by a stroke with a 69.
After his round McIlroy refused to climb down on his Wednesday remark that the Ryder Cup was an exhibition match, over which Montgomerie had disagreed vehemently. The pair did not discuss the issue during the round, though, McIlroy said.
The 1999 British Open champion Paul Lawrie is in a large group in third place, three shots behind Molinari.