The two-time Ryder Cup player kept a bogey off his card and, after 18 holes at La Quinta, is a shot adrift of American Michael Putnam.
The 32-year-old, world No 56, from Turin played in the 2010 and 2012 Ryder Cups but missed the match at Gleneagles last September and this was the reason why he decided to open his season on the PGA Tour in 2015.
Following his round over the Palmer Course, he said: “I was disappointed to miss the Ryder Cup and I thought that starting the year in the States might be good and we???ll see if it pays off.”
Molinari, whose highest-ever finish in a PGA Tour event is third, is one of five players tied-for-second behind Putnam who needed just 29 strokes to complete the back nine.
The 31-year-old Putnam, chasing a first-ever title, was playing the Jack Nicklaus Private Course at PGA West and was level par after six holes before starting on a birdie blitz of nine birdies in 12 holes – including six in a row.
He said: “You have to mentally throw this one away because you’re not going to play the Nicklaus again.
“The focus for me is on the Palmer on Friday and then La Quinta on Saturday. There are a lot of birdies going to be made in 54 holes by a lot of guys. So I have to make a lot of birdies too.”
But a slow start for 44-year-old Phil Mickelson whose 71 at La Quinta has left him in a tie-for-89th.
Leftie made three birdies as he reached the turn in 33 strokes before stuttering on the back nine as he posted three bogeys in the space of five holes.
He said: “I got off to a pretty good start and then I just stalled.
“I can’t wait to get started again because I feel like I played a little tight today, kind of steered it a little bit.???