They upstaged Simone Manuel, who claimed the top podium for the United States in the women's 100m freestyle. She had shared Olympic gold at the Rio Games last summer, but took the medal outright this time, beating top-ranked Sarah Sjostrom of Sweden.
Sjostrom had gone under the 52-second barrier in the 4x100m relay and was again under world-record pace at the turn. But Manuel, a 20-year-old Texan, clawed her way level with 25m left and with her final five strokes clocked an American-record time of 52.27 seconds.
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Sjostrom finished 0.04 seconds back. Denmark's Pernille Blume took bronze.
Among the Russians, Chupkov overhauled his Japanese rivals to claim men's 200m breaststroke gold in two minutes 06.96 seconds. Yasuhiro Koseki and Ippei Watanabe, the world record holder, had traded leads throughout before Chupkov produced a winning burst in the final 50m.
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Watanabe took silver and Koseki bronze.
Earlier, Rylov had set a European record, beating Olympic champion Ryan Murphy of the United States in the men's 200m backstroke. Rylov stole a march on the opening 50m and held an unassailable lead thereafter, winning with a time of one minute 53.61 seconds.
Murphy settled for silver and his compatriot Jacob Pebley took bronze. Another Olympic champion, Xu Jiayu of China, finished fifth.
Efimova then matched Alexsandr Popov's five individual world titles for Russia with a gold in the women's 200m breaststroke. She came in 0.53 seconds outside the world record.
Bethany Galat of the United States finished second, over two seconds back. Shi Jinglin of China won bronze.
Britain defended its world title in the 4x200m freestyle when James Guy propelled the team to gold ahead of Russia. The United States edged Australia for bronze.
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Great Britain defends 4x200m freestyle relay title at World Championships