Feild prevailed at the San Antonio Stock Show and Rodeo, propelling him into second place on the early-season money list.
Meanwhile, Wright won at the Fort Worth Stock Show and Rodeo to grab the lead in the saddle bronc standings.
The top 15 money-winners in each event qualify for the National Finals Rodeo, which is held in December at the Thomas & Mack Center in Las Vegas.
In San Antonio, Feild stole the show.
After drawing a highly regarded horse named Multi-Chem Brother in the championship round, he set an arena record with a score of 93.
Feild missed the Professional Rodeo Cowboys Association world record by one point.
According to the PRCA website, Feild talked to Jessy Davis, another Payson bareback rider, about Multi-Chem Brother before the final round.
Davis had posted scores in the 90s on two previous efforts aboard the horse and told Feild he'd gotten a good draw.
He was looking at a score of at least 90, if he managed to stay aboard, according to Davis.
" I was going to bear down and go for the win," Feild said, "and it turned out pretty well."
After his victory in San Antonio, Feild celebrated with the crowd.
"Man, that's pretty awesome," he said. "I don't like being in front of an audience, but I'd like to do that again. That was pretty neat."
Feild's performance also marked a high point in the feel-good comeback of Multi-Chem Brother.
The horse suffered a pastern joint injury last year at Odessa, Texas, but is healthy again and competing again after surgery.
So far this year, he has already earned $28,795, pushing him over $500,000 for his career.
Feild finished fifth in the world in 2010 despite missing two months with a broken arm that required surgery.
Like Feild, Wright got his new season off the momentum-building beginning in Texas.
At Fort Worth, he scored a 91 on his third of three rides aboard a horse named Tipped Off to win the average title at the $557,000 rodeo.
"It feels awesome," Wright said. "That was a great horse. I'll never get tired of getting on horses like that."
Wright has earned $39,781 this season. He is attempting to qualify for the ninth National Finals of his career and capture his third world championship in four years.