Harris, from Mullin, Texas, earned $18,257 to move from second to first with $170,886.
Previous leader Cody Teel of Kountze, Texas, one of only five cowboys with successful first-round rides, finished fourth with a 74.5 on Gauteraux's Iron Horse. He has earned $167, 225.
In tie-down roping, defending world champion Tuf Cooper of Decatur, Texas, took a big step in his bid to repeat by winning in 7.4 seconds. Cooper is second in the world standings with $142,679.
Justin Maass of Giddings, Texas, tops the list with $144,001. Maass was shut out in the round after failing to place among the top six.
In saddle bronc riding, defending world champion Taos Muncy of Corona, N.M., won with an 87 on Fire Lane. He's second in the season standings with $118,998.
"That horse was real good and it took two jumps, and I got a pretty good mark-out on him," Muncy said. "After the first two jumps, he stayed underneath himself and was really an awesome horse that I'd like to get on every day."
Jesse Wright of Milford, Utah, stayed in first at $145,760 by tying for second with brother Jake at 84.5. Jesse Wright rode Going South, while Jake was on Spring Blues. A third Wright brother, Cody, placed fourth with an 83.5 on Lori Darlin.
In bareback, Wes Stevenson of Lubbock, Texas, won with an 87 on Freckled Doll. Kaycee Feild of Payson, Utah, the standings leader with $149,295, was fourth with an 84.5 on Short Fuse.
Stevenson, making his eighth NFR appearance, is seeking his first world championship.
"I'm pretty pumped. It's an important win," Stevenson said. "But a guy needs to keep doing good. Every single time I come here, it's a new experience. I don't get much butterflies anymore, but I do here."
Defending world champion Feild widened his lead over second-place Steven Dent of Mullen, Neb., who didn't place among the top six. Dent remained second at $140,781.
In steer wrestling, Casey Martin of Sulphur, La., won with a 3.4-second run. Dean Gorsuch of Gering, Neb., was second at 3.5. World leader Ethen Touvenell of Napa, Calif., followed in third in 3.6 to push his total to $109,591.
In team roping, header Kaleb Driggers of Albany, Ga., and heeler Jade Corkill of Fallon, Nev., tied with header Brock Hanson of Casa Grande, Ariz., and heeler Ryan Motes of Weatherford, Texas, at 4.7.
Header Trevor Brazile of Decatur, Texas, and heeler Patrick Smith of Lipan, Texas, remained in the world lead with $144,649 for Smith and $143,149 for Brazile by finishing third in 4.8. Driggers, who has earned $126,571, and Corkill, who has made $122,480, are the second-place team.
In barrel racing, Mary Walker of Ennis, Texas, in 13.75 to move up to second in the standings with $145,549
Leader Brittany Pozzi of Victoria, Texas, placed third in 13.86. She has earned $181,856.
In all-around, defending world champion Brazile, who has won nine of the last 10 world all-around titles, extended his lead over runner-up Dent. Brazile has earned $258,873, while Dent has made $144,465.