The 33-year-old Stuard had only 21 putts in his bogey-free round at TPC Louisiana, finishing his final hole after a rain delay of nearly five hours. He's winless on the PGA Tour.
None of the afternoon starters were able to finish before darkness suspended play.
Retief Goosen was second after a 65. The 47-year-old South African is a two-time U.S. Open champion.
Top-ranked Jason Day bogeyed his final two holes for a 69. The Australian is the first No. 1 player to play in the event since David Duval in 1999.