Americans Trey Mullinax, Daniel Berger, Luke List, Ryan Moore and Ryan Palmer were all one shot back.
World number one Dustin Johnson mixed four birdies with a lone bogey for a three-under 68 that left him in a share of 15th.
Molinari, who took a two-shot lead into the final round at Augusta National before a pair of double-bogeys on the back nine opened the door for eventual winner Tiger Woods, was nine shots back of leader Lowry.
The British Open champion began his day at the par-four 10th and mixed a double-bogey with four bogeys and three birdies en route to a three-over-par 74.
Other notables in the field include three-times major champion Jordan Spieth and Englishman Tommy Fleetwood, who each carded even-par 71s.
(Reporting by Frank Pingue in Toronto; Editing by Peter Rutherford)
