Clarke, one behind overnight, managed only a front nine 40 in the windy conditions, paying a heavy price for trying to play his ball out of the edge of the water on the long third.
It took the 41 year old three attempts to find the green and after a double bogey seven there he three-putted the short fifth.
That opened the five shot gap between the two, but Molinari bogeyed the sixth and seventh.
They turned at 13 under par and ten under respectively, with Molinari's younger brother Francesco two further back in third.
Molinari's advantage became four again when Clarke failed to find the green on the short 11th and missed a six foot par putt to slip further back to nine under.
A 15 foot putt on the 14th took Molinari five clear for the second time in the day, but a mishit drive down the next forced him to take a penalty drop.
He could still only chip out and with a double bogey six the lead was back down to three.