Castle stuart, Scotland, July 12, 2012 (AFP) - Molinari, 29 birdied five holes in a row from his fifth and then four in succession from his 12th in a bogey-free display that is two strokes fewer than the previous low set in the event a year ago.
The London-based Italian's round comes also just four days after he shot a final round 64 to grab second place in the French Open.
"It felt quite easy today but then it's not as easy as it looks but I was feeling comfortable on the golf course," he said.
"I had a terrible day on the greens in Paris last Saturday but had a good session on the practice putting green Saturday evening.
"Sunday was just brilliant, and today I just kept it going. I know it's not going to keep going for much longer, so I'll enjoy the moment."
Spain's Alejandro Canizares birdied his closing six holes to move into second place on six under par and one clear of the duo of Denmark's Soren Kjeldsen and Frenchman Raphael Jacquelin.
Jacquelin, who was third in last week's French Open, started his round with three straight birdies and then birdied two of his closing three in his equal-best score in 48 rounds of Scottish Open competition since making his debut in 1998.
World number one and defending champion Luke Donald started his round with four straight birdies but spoilt his momentum with bogeys at five and eight before three further birdies over his last six holes.
This week is Donald's first event since missing the US Open halfway cut with a shock 11-over par 36-hole tally.
"It was a great start and I could not have asked for better but that was a sloppy bogey at eight that halted my momentum," he said.
"Overall, it's a pretty satisfying start after being away from the game for three weeks. So to come back and find some form pretty early on is encouraging."
Triple Major winning Ernie Els was met by a Tour referee after his round of a two under par 70 following an incident at the sixth hole where the South African took four shots to get out of a bunker in taking a double bogey seven.
A person watching TV coverage of the event phoned the Tour complaining Els may have broken the rules while in the bunker.
The Tour looked at video footage of the incident while Els continued to play his round but then advised him on handing in his card there had been no breach of the rules.
"Some viewer called in to say I did something that I didn't do and he thought I was kicking and screaming which I wasn't but there was no penalty," said Els.
"But that would have been a world record for me to be 10-feet from the green in two and to have walked off with a nine but then a seven in bad enough.
"I was just getting in some bunker practice at six for The Open. I was starting to get embarrassed there. I am sure some links golf course has got me in the past but the first lie was pretty horrendous as it was lying down and I was just trying to hit it out to the left.
"Then it was just a case of me digging a grave but I managed to put that out of the way and then played some decent golf."
England's Andrew Johnston was celebrating a first Tour hole-in-one when he aced the par three 11th hole on route to a three under par 69.
Johnston earned himself 168 bottles of French champagne, and one bottle for each of the 168 yards of the par three.
Leading first-round scores on Thursday in the European PGA Tour Scottish Open (par 72):
62 - Francesco Molinari (Italy)
64 - Alejandro Canizares (Spain)
65 - Soren Kjeldsen (Denmark), Raphael Jacquelin (France)
66 - Shane Lowry (Ireland), Robert Coles (Britain), Peter Lawrie (Ireland), Fredrik Jacobson (Sweden), Alexander Noren (Sweden), Andrew Marshall (Britain), Jeev Milkha Singh (India)
67 - Pablo Larrazabal (Spain), Luke Donald (Britain), Oscar Floren (Sweden), Anthony Wall (Britain), Martin Kaymer (Germany), S.S.P. Chowrasia (India), Matthew Baldwin (Britain)