The 29-year-old leads the Aberdeen Asset Management Scottish Open after a 10-birdie course record 62 at Castle Stuart against a field that included world number one Luke Donald and 10 major champions.
Edoardo won the title at Loch Lomond two years ago, three months before he and Francesco became partners in the Ryder Cup.
But the older of the pair had left wrist surgery two weeks ago and, having not played for a month, is likely to spend the entire summer rehabilitating.
"It would be nice to do well this week for him as well - to cheer him up a little bit," said Francesco, who looks in the form of his life after finishing second in the French Open on Sunday thanks to a closing 64.
If he wins this weekend it would be only the second time in European Tour history that brothers have won the same event. Spaniards German and Antonio Garrido were Madrid Open champions in 1973 and 1977, respectively.
At 10 under after 15 holes, Molinari - on course to earn a second cap against the Americans in September - admits he did work out that three more birdies would give him the circuit's first-ever 59.
It did not happen - he parred them all - but he can still claim to have broken 60 for 18 holes. In Paris he played his last nine in 29 and here he turned in 30.
The 62 matched the lowest round of his Tour career and was a far cry from his first experience of links golf.
That came in an amateur event at St Andrews over a decade ago. Anybody seeing him give a fist-pump of celebration when he birdied the last would have thought he had had a good day - but it was to break 90.
Not that he was the only one to suffer that day. One of his partners had "10 or 11" attempts to get out of a bunker on the short eighth, gave up and walked in.
Molinari is now a Ryder and World Cup winner, also has a world championship victory to his name, and will see his odds for next week's Open Championship cut even more - he is currently around 40/1 - if he goes on like this.
"I know it's not going to last for ever," he added, "but I hope to keep this going a little bit longer - obviously next week, but the next month or so is really big for the Ryder Cup.
"That, probably more than The Open, is in my mind."
Molinari, whose start is the best of the Tour season, finished the day two in front of Spaniard Alejandro Canizares and three clear of Frenchman Raphael Jacquelin - third in the French Open last week - and Dane Soren Kjeldsen.
Canizares was only one under at the turn, but covered the front nine in a seven under 29, finishing with six successive birdies.
Donald was flying as well until he bogeyed two of his final five holes for a 67, but there were some big names who would have been delighted with that start.
Late entry Phil Mickelson, who left his family on holiday in Rome because recent poor form had left him feeling the need for another tournament before The Open, managed only a 73, the same as Scotland's top-ranked player Paul Lawrie.
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Alongside them is 21-year-old Tom Lewis, whose hopes of returning to The Open a year after he shot the lowest-ever round by an amateur and led are now hanging by a thread.
Lewis has sought help from Mickelson's coach Butch Harmon during a run that has seen him make only one of his last six cuts, but only a top five finish will get him to Lytham.
The struggles of Paul Casey continue as well. Joint last after back-to-back 80s in Paris, the former world number three shot 76 and is close to last.
He has made only one cut since dislocating his shoulder snowboarding in Colorado on Christmas Eve.
Padraig Harrington returned a 69 and Ernie Els a 70 that included four in a bunker for a double bogey seven at the long sixth.
England's Andrew Johnston's 69 included a hole-in-one on the 168-yard 11th that won him 168 bottles of champagne.
"I think I'm going to have to give quite a few away or I'll turn into an alcoholic," he said.