The pair carded first-round scores of 66 to finish on six under par - one shot clear of Scotland’s Martin Laird.
Gonzales picked up three shots during his first nine holes - at the first, fifth and seventh - and collected further birdies at the 11th, 14th, 17th and 18th holes. His round was spoiled, albeit only slightly, by a bogey at the 12th.
Korean Bae matched his American rival by picking up seven shots in his round - including three consecutive birdies at the last three holes. He too needed five shots at the 12th to bogey the hole.
Laird carded five birdies in a round of 67 to trail the leaders by one shot, while Americans Charlie Beljan, Luke Guthrie, Colt Knost, Brooks Koepka, Kyle Reifers and Jon Curran were part of a nine-strong group a further shot back on four under.
Former world number one Vijay Singh dropped four shots on the back nine to sign for a level-par score of 72, while Lee Westwood recorded four bogeys in a one-over-par score of 73.
Defending champion Jimmy Walker was nine shots off the pace after posting a three-over 75.