After a fog delay of more than three hours, Molinari's four under par 68 put him alongside left-hander Bubba Watson.
"It was a pretty solid round," said Molinari. "I hit the ball quite well all day and basically just tried to stay out of trouble and get some birdies here and there when I had the chances.
"So I think today everything was going pretty much according to the plan, but obviously the week is very long and it's not going to be so easy for me all week."
When play was called off because of fading light just before 8pm local time, South African Ernie Els and Americans Matt Kuchar and Nick Watney were on the same mark entering the closing stretch - with Northern Irishman Darren Clarke and England's Simon Khan among those only one behind after 13 and seven respectively.
Clarke is making his return to the venue where he led six years ago after a course-record 65, while Khan, of course, won the BMW PGA Championship at Wentworth in May.
"I played nicely for the most part today," said Clarke. "I played sensibly to the middle of the greens much of the time and attacked a bit with wedges in my hand.
"The course is fantastic and it is always nice to come back to one where you have played well on before. That's the same for everybody. It's a lot different to then though as it is softer and the greens are holding and it wasn't quite that way last time we were here."
Molinari, currently eighth on The Ryder Cup points table, birdied three of his last five holes to catch Watson and said: "I try not to think about The Ryder Cup.
"I was playing well in practice, so I just said to myself 'try to focus on doing as good as you can in this tournament and then see what happens'."
One behind in the clubhouse are Australian Jason Day and American duo Charles Howell III and Ryan Moore after three under par 69s. Gonzalo Fernandez-Castaño is on the same mark with two to play along with Khan and 41 year old Clarke, who had a hat-trick of birdies from the ninth - the last of them after an expert chip-and-run to two feet.
“I'm very happy with my tee to green performance, I left myself a lot of birdie opportunities,” said Spain’s Fernandez-Castaño. “Unfortunately I wasn't that confident with my putter. I was like almost not getting it to the hole with my putter and that's probably what you expect coming from Europe, you expect to get really fast greens and maybe they weren't that quick today.”
Unlike last week's World Golf Championships-Bridgestone Invitational, meanwhile, Tiger Woods is in touch with all the leaders and on the comeback trail.
Only joint 78th out of 80 in Akron - and 18 over par in the process - Woods posted a one under par 71.
Woods raised hopes of a stunning turnaround in his fortunes when he birdied three of his first four holes and shared the lead.
He dropped back to level par with bogeys on the 15th - his sixth - the long second and short seventh, but raised his morale again with a closing birdie.
Woods commented: "I hit the ball pretty good and I felt like I had control - my trajectory was nice and I've not had in a while.
"I just need to keep improving every day."