Guy Allen holds the record with 18 season championships, all in steer roping.
If Brazile, from Decatur, Texas, and heeler Patrick Smith, from Lipan, Texas, win another round, Brazile will match Billy Etbauer's record of 51 NFR victories.
Brazile also is trying to become the first cowboy to win multiple world championships in four categories. He has 10 all-around titles, three in tie-down roping, three in steer roping and one in tie-down roping.
"It's just such a relief," Brazile said about winning the all-around title. "As much as I try not to let it affect anything, it kind of just releases me to go try to do whatever it takes to win the team roping and just concentrate on that title. That is the immediate thing that I think about. And as far as the long-term stuff, 10 world titles is more than I ever could have dreamed of. It's awesome."
Brazile pushed his all-around total to $298,626.
In team roping, Brazile and Smith finished second in 4.1 seconds in the sixth round. Brazile has earned $182,903 in the event, and Smith tops the heelers with $184,403.
Header Kaleb Driggers of Albany, Ga., second with $145,123, and heeler Jade Corkill of Fallon, Nev., who has made $141,032, were shut out in the round by failing to place in the top six with their run of 4.4.
Header Colby Lovell of Madisonville, Texas, and heeler Russell Cardoza of Terrebonne, Ore., won in 3.7.
In barrel racing, Mary Walker of Ennis, Texas, finished second in 13.76 seconds to take the season lead with $204,149. Previous leader Brittany Pozzi of Victoria, Texas, who didn't finish among the top six, dropped to second with $191,280.
Walker also leads all NFR competitors with $76,857 during the first six rounds. Kaley Bass of Kissimmee, Fla., who was fourth in 13.90, tops the NFR aggregate standings at 83.86 for six rides.
Carlee Pierce of Stephenville, Texas, won the round in 13.51.
In bareback riding, the first rider to compete won for the second straight round, with NFR rookie Winn Ratliff scoring 83.5 points on Star Burst.
"I was kind of nervous," Ratliff said. "Casey (Coletti, the fifth-round winner) bumped off 88.5 points and I only got an 83.5. I was a little tense because usually when you're the gunner, you don't score high. It becomes a sit-and-wait game. I was crossing my fingers. But it comes down to not worrying about how everyone else did, just concentrating and focusing on what you did."
Standings leader Kaycee Feild of Payson, Utah, finished in a four-way tie for second with an 82.5 on Outa Sight. Defending world champion Feild has earned $201,073, while Will Lowe of Canyon, Texas, who didn't place among the top six, remained second with $163,142. Feild also leads the NFR aggregate standings with 506 points.
In steer wrestling, three-time and defending world champion Luke Branquinho of Los Alamos, Calif., remained atop the standings lead for the second day in a row with $132,755 after placing fifth in 4.3. Ethen Touvenell of Napa, Calif., finished fourth in 4.2 to move up from third to second in the standings with $120,192.
Two-time world champion Dean Gorsuch of Gering, Neb., dropped from second to third with $116,067 after failing to finish in a money position.
Les Shepperson of Midwest, Wyo., and Gabe Ledoux of Kaplan, La., tied for first in the round at 4.0.
In saddle bronc riding, Wade Sundell of Boxholm, Iowa, and Taos Muncy of Corona, N.M., tied for first at 84. Sundell rode Lori Darlin, and Muncy was on Flaming Desire.
Sundell moved into second place in the NFR aggregate standings with 414.5 points over five rides. He also remained second in the standings with $163,458.
Jesse Wright of Milford, Utah, who placed fourth with an 81.5 on Round Robin, tops the standings at $188,016.
Cody DeMoss of Heflin, La., who didn't finish among the top six, leads the NFR aggregate standings race with 472.5 points for six rides. He's the lone competitor with six successful rides.
In tie-down roping, Clint Robinson of Spanish Fork, Utah, and Ryan Jarrett of Commanche, Okla., tied for first at 7.2.
Tuf Cooper of Decatur, Texas, remained the standings leader after failing to place among the top six. Cooper has earned $176,543, while second-place Justin Maass of Giddings, Texas, who also didn't place among the top six, has made $170,798.
In bull riding, J.W. Harris held on to the standings lead despite being bucked off. Harris, from Mullin, Texas, has earned $192,971, while Cody Teel of Kountze, Texas, who also failed to stay on his bull, remained second with $185,782.
Beau Schroeder of China, Texas, won the round with an 89 on Feeling So Fly. Schroeder leads the NFR aggregate standings race with four successful rides for 343.5 points, while Seth Glause of Cheyenne, Wyo., was second with four rides for 336 points.