The only team-based tournament on the PGA Tour schedule, the Zurich Classic uses a four-ball (best-ball) format in the first and third rounds, and foursomes (alternate shot) in the second and final rounds.
"Both of us played nicely, and we probably ham-and-egged it just about perfect, right?" Hossler said of the 11-under-par 61 he and Clark carded at TPC Louisiana.
There are five teams tied for third at 10 under, including brothers Matt and Alex Fitzpatrick of England.
US Open champion Matt Fitzpatrick won the RBC Heritage on Sunday, while sibling Alex is making his second career start on the PGA Tour.
Hossler got the first-time teammates started with a birdie at the par-4 first hole, and added further birdies at Nos. 6, 9, 11, 12, 13 and 16.
Clark backed him up with birdies at holes 3, 7, 15 and 18, as well as making par on No.10 to erase Hossler's bogey.
"We took advantage of the hardest holes, which is not easy to do out here," Hossler said.
"With that said, we left a couple out there that hopefully we can get in the next few days."
O'Hair and Matthews also tore through the course, with a 30 on the front nine and a 31 on the back nine, including Matthews' eagle on the par-4 12th hole.
"I just kind of filled the gaps," O'Hair said.
"The way (Matthews) hits the driver is unbelievable, and it just puts him in so many good scoring positions. It was fun to watch, really."
Joining the Fitzpatricks in the tie for third are the teams of David Lipsky-Aaron Rai, Keith Mitchell-Sungjae Im, Luke List-Henrik Norlander, and Michael Kim-S.Y. Noh.
Defending champions Xander Schauffele and Patrick Cantlay are tied for 56th at 5-under 67.
A shot further back in a tie for 68th are Australian pair Greg Chalmers and Cameron Percy, along with Geoff Ogilvy and his playing partner Kevin Stadler of the US.
Aaron Baddeley and Harrison Endycott finished day one at 2-under in a tie for 76th.
Of the 80 teams, 79 finished at 1-under 71 or better.
The lone duo above par were major champions John Daly and David Duval, who came in at 3-over 75.
