Byrne, of Prince Albert, Sask., scored an 88.50 and tied with Brazil's Fabiano Vieira for Monday's best scores.
Byrne, Mike Lee of the United States, Aaron Roy of Yellow Grass, Sask., and Dakota Buttar of Kindersley, Sask., all advance.
Roy was the only other rider to finish the fourth performance — scoring an 86.50.
Tanner Milan of Cochrane, Alta., was the top Pool A steer wrestler. He had the third best score on Monday at 4.2, but success in his previous three performances has him at the top of the standings.
Clint Laye of Cadogan, Alta., struggled in his final bareback performance, but was good enough to finish first in the Pool A standings. Laye had a 73.00, much less than Regina's Ty Taypotat, who scored an 84.00 in the fourth performance.
Laye, Taypotat, Kyle Bowers of Brooks, Alta., and Luke Creasy of Brownfield, Alta., all advanced.
American Blair Burk captured the tie down roping, with a 7.7 in his fourth performance while Mary Walker, of the U.S., was first in the ladies barrel racing.
U.S. rider Rusty Wright won the saddle bronc after an 89.00 in his fourth performance.
Pool B competition starts on Tuesday.