Smith's 68 left the one-time world No.2 leading the Australian challenge, six shots behind record-setting American leader Xander Schauffele.
He lamented not going lower but, after battling an uncooperative blade and still tying for sixth at the Masters, Smith was pleased enough with his opening to the year's second major championship.
"I actually hit the ball quite well for probably the first 12 or 13 holes there," Smith said.
"Kind of let go of it a little bit at the end, but everything felt really good and I managed to get a few good par saves and keep the momentum going for tomorrow."
Some much needed R & R was the priority before what he expected to be a gruelling last three rounds at the challenging 7609-yard layout in Louisville, Kentucky.
"It's going be a long week," Smith said.
"I think you know that at the start of the week anyway - it's a major week. It's always more demanding.
"So plenty of rest this afternoon, maybe hit a few balls, clean some stuff up and get a good sleep tonight."
After starting on the 10th tee, Smith collected four birdies in his first 13 holes to try and hunt Schauffele down.
But he drove into the native area on the par-4 fifth to record his day's only blemish before scrambling home with four straight pars to sit in a share of 15th.
He said patience was the key to reeling in Schauffele.
"You just have to hit the fairway," Smith said.
"It's definitely long but there's still a good mix of holes where you still get a lot of wedges, a lot of short irons and, even for myself, I feel like I'm able to make some birdies out there.
"So it would help to hit it another 20 or 30 yards, but I don't think you have to hit it too far."
Smith's LIV Golf teammate Lucas Herbert was the next best Australian after signing for a two-under 69.
"Everything was kind of decent but nothing was amazing," Herbert said.
"Got off to a poor start there but then caught that back up with four birdies.
"I think I holed out really well, holed some nice five footers, some sort of eight footers just to keep my momentum through the round, through the back nine and not drop any shots when I maybe struggled a bit."
It was a challenging day for Adam Scott and Australia's afternoon starters.
Jason Day mixed four birdies, including one at the last, with four bogeys in an even-par 71.
Min Woo Lee shot 72, as did Scott, who never got going in matching his playing partner Tiger Woods' opening round.
Scott failed to make a single birdie but limited the damage with a lone bogey on the par-3 14th, his fifth hole of the day.
Coming off an impressive tie for 12th at the Masters, Cam Davis had a shocker, posting a seven-over 78 to be next to no chance of making the halfway cut.