Defending champion Justin Rose, the highest-ranked player in the field at No. 3, shot 74 as all five of the top-10 players competing at Hogan's Alley finished over par.
Finau hasn't finished better than 60th in three tournaments since tying for fifth at the Masters. He had five birdies over seven holes and avoided a second bogey with a chip-in at the par-3 16th.
Spieth is trying to end a victory drought that's approaching two years for the three-time major winner.
The 2016 Colonial champion kick-started his round by chipping in for birdie on the par-3 13th, his fourth hole. Spieth had seven birdies in a 10-hole span that included a double-bogey.