Leyva became the first U.S. men's world champion since Paul Hamm's floor exercise win in 2003 with a victory in the parallel bars. He scored 6.400 in difficulty and an impressive 9.233 in execution for a total of 15.633.
That was 1-10th of a point ahead of China's Zhang Chenglong and Greece's Vasileios Tsolakidis, who tied for second.
Sui had the highest scores in both difficulty (6.600) and execution (9.266) in winning the balance beam with a point total of 15.866. Her Chinese teammate Yao Jinnan was second at 15.233 and Jordyn Wieber, the women's all-around champion earlier in the competition, was third at 15.13.
Sui was the runner-up in the floor exercise. Russian gymnast Kseniia Afanaseva claimed the gold in the event with a score of 15.133, edging Sui (15.066) on execution points. American Alexandra Raisman (15.000) took the bronze medal.
South Korea's Yang Hak-seon totaled 16.866 points in winning the men's vault. Russian Anton Golotsutskov was second at 16.366 and Japan's Makoto Okigucki was third at 16.291.
China's Zou Kai, who took silver in the floor exercise Saturday, won the gold medal in the high bar as Zhang again just missed finishing first. Zou had a score of 16.441 to Zhang's 16.366. Japan's Kohei Uchimura (16.333) took the bronze to go with his golds in the all-around and floor exercise.