TOKYO—Team USA swimmers on Sunday raced to their best-ever start at an Olympics, winning medals in every event of the first finals session, including the first U.S. gold medal of the games in any sport.

Team USA’s six medals—one gold, two silver and three bronze—are the most it’s ever won on the first day of Olympic swimming finals. It’s even more impressive considering that prior to 1984, countries could send three swimmers per event instead of two, allowing possible podium sweeps.

The team made the podium in events in which it wasn’t supposed to medal, said U.S. men’s team assistant coach Jack Bauerle. “It’s obviously a really proud moment,” he said. “I can’t really feel anything, I’m so happy.” 

Things started with a bang in the men’s 400-meter individual medley as Chase Kalisz, a former world champion in the event, won gold in 4:09.42. His former college teammate and training partner at the University of Georgia Jay Litherland surged in the final 75 meters of the freestyle leg to touch second in 4:10.28.

Kalisz noted that his winning time was considerably slower than the 4:07.75 he swam en route to a silver medal at the 2016 Rio de Janeiro Olympics, but was unsurprised given the flipped competition schedule in Tokyo. To accommodate television viewers stateside, preliminary sessions here take place at night while swimmers compete for medals in the morning—the opposite of how most international meets typically are organized.

The schedule changes did not appear to slow the U.S. during the remainder of the session. In the men’s 400 freestyle, Kieran Smith won bronze in 3:43.94 behind Australia’s Jake McLoughlin and Ahmed Hafnaoui, an 18-year-old from Tunisia who won a surprise gold from lane eight.

Emma Weyant and Hali Flickinger won medals in the 400 individual medley.

Emma Weyant and Hali Flickinger won medals in the 400 individual medley.

Photo: David Ramos/Getty Images

Two more Americans got on the podium in the women’s 400 individual medley. After swimming the top qualifying time on Saturday, 19-year-old Emma Weyant took silver in 4:32.76 behind Yui Ohashi of Japan, who won the host country’s first gold medal in the pool. Teammate Hali Flickinger took bronze in 4:34.90, making it the first time in more than 50 years that two American women have medaled in the event.

Team USA’s final medal of the session, a bronze in the women’s 4×100 freestyle relay, was it’s least likely, after the team qualified fifth on Saturday night. U.S. women’s team coach Greg Meehan took a gamble by giving the anchor spot to Simone Manuel, the defending gold medalist in the women’s 100 freestyle who failed to make the final of the event at the U.S. Olympic Swim Trials in June. 

Manuel said she has suffered with “overtraining syndrome”—a condition where athletes experience fatigue, elevated heart rates and declining performance during usual training—this year, but was “feeling better” in Tokyo. She turned in the second-fastest split for the Americans, who finished 0.03 seconds behind Canada in 3:32.81. Australia broke the first world record of the meet, swimming 3:29.69 en route to gold.

Write to Laine Higgins at laine.higgins@wsj.com