Both players shot 5-under 67 on Saturday.
It is the first time that either player has been at the top of the leader-board through 54 holes. They have a one-shot lead over Philip Archer (68), who was a co-leader after Friday's second round.
Archer is 15-under 201.
Nicolas Colsaerts of Belgium had the day's lowest round -- an 8-under 64 -- to jump from 38th into a tie for fourth at 14-under 202.
On Sunday, Molinari, who has strong backing from the crowd in his native Italy, will be gunning for the first Italian Open title by an Italian in 26 years.
"I am happy to be here and have the support of the crowd," Molinari said. "Hopefully we can do it (Sunday). I was quite nervous."
Swim Week Miami Beach 2014 [PHOTOS]