Stallings, a three-time winner on the PGA Tour, had a 66 to match Thompson at 16-under 197 at Hillcrest in the second of four events that will determine 25 PGA Tour cards for next season.
"I was hitting my mid- and short irons really well, my wedges really well, and gave myself a lot of chances for birdie inside 15 feet," Thompson said. "Especially on the back nine, I made basically every putt inside 15 feet except for the last one. You can't complain when that happens, and I've been struggling with my putting, so this is really nice to see and it gives me some confidence going forward."
Stallings birdied six of the first 11 holes but made a bogey at the par-4 12th and pars at the drivable 15th and reachable par-5 16th. He closed with a birdie on 18.
"I felt like a really, really good one that kind of got away from me," Stallings said. "I got off to a really good start, didn't play the par 5s particularly well, but I kind of managed my game as good as I could. I drove it in rough a few times on the scoring holes, and then kind of got some weird breaks. But it was nice to finish with a birdie."
The series features the top 75 players from the Web.com money list, Nos. 126-200 in the PGA Tour's FedEx Cup standings -- Stallings was 128th, Thompson 145th and Carballo 187th -- and non-members such as Johnston with enough PGA Tour money to have placed in the top 200 in the FedEx Cup had they been eligible.
The top 25 players on the Web.com regular-season money list earned PGA Tour cards. They are competing against each other for tour priority, with regular-season earnings counting in their totals. The other players are fighting for 25 cards based on series earnings.