A bogey at the last hole, after finding the water left of the green, cost Smith outright second place and he now shares that position with Jon Rahm, Patrick Cantlay and Billy Horschel.
Smith has shown improvement in recent weeks after a disappointing few months, a decision to adopt a less technical approach to his game now appearing to pay dividends including a good week at the Open Championship last week.
After his opening round of 65 yesterday, Smith today worked towards the early lead held by Fitzpatrick (who had finished his round in the group ahead) before his dropped shot at the last, but he is well placed heading into the final 36 holes.
Marc Leishman and Adam Scott are at 2 under and tied for 22nd place, Jason Day is at 1 over and in 36th place in the 63 player field.
The leader, Fitzpatrick, who is playing this venue for the first occasion, was out in the first group on day two, a final nine of 31 and a round of 64 allowing him to take the clubhouse lead and hold off all challengers throughout the afternoon.
Fitzpatrick is seeking his first PGA Tour victory but earlier this year he did finish runner-up at the Arnold Palmer Invitational and has played well in recent weeks.
Interestingly, both he and Smith tied for 20th at Royal Portrush last week.
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