Fitzpatrick went bogey-free around the difficult Jack Nicklaus layout, whereas Simpson made seven birdies and a single bogey to tie for the top spot at 6-under.
Here's how the top of the leaderboard stands following Day 1:
|Place||Player||To Par||R1 Score|
Rory McIlroy ranked 57th out of the field's 72 golfers in strokes gained putting for Round 1 but still shot 3-under.
The scoring average for the field, which consists of 47 of the top-50 golfers in the world, was 71.99. The par at The Concession Club is 72.