Top-ranked Yi won the women's 10-meter air rifle while Sylwia Bogacka of Poland took silver and China's Yu Dan the bronze.
In the swimming heats at the Aquatic Centre, Phelps, who won eight gold medals at the Beijing Games four years ago, qualified only eighth-fastest for the night final of the 400-meter individual medley.
"That one didn't feel too good," he said.
Olympic champion Park of South Korea won his 400 freestyle heat, but was disqualified for a false start. Paul Biedermann of Germany, the world record holder in the event, failed to make the final.
Phelps, the two-time defending Olympic champion won his heat in 4 minutes, 13.33 seconds with a time that was well off his world record of 4:03.84 set four years ago in Beijing.
But it was only good enough to secure the last spot in the evening final, when Phelps will swim in lane one instead of the middle of the pool.
"The only thing that matters is just getting a spot in," he said. "You can't win the gold medal from the morning."
Three other finals were scheduled in swimming on Saturday night— the women's 400 IM, men's 400 freestyle and the women's 4x100-meter freestyle relay.
The cycling road race got underway Saturday on the first full day of competition, and, with it, Britain's best chance for an early gold medal.
Mark Cavendish, riding alongside fellow Briton and Tour de France winner Bradley Wiggins, was among the starters for the 250-kilometre race which passes some of London's most iconic landmarks. Huge crowds lined the course.
British team manager Dave Brailsford said Cavendish was the focus of his team.
"There's no doubt they are riding for one rider," Brailsford said. "They've got no aspirations for themselves. It's all for Cav. We have all our eggs in one basket."
After Prince Charles was introduced to the British team, the race started on a processional pace from the Mall, with the peloton heading southwest through the city.
In a later shooting final, Tan Zongliang of China was hoping to underscore his No. 1 ranking in 10-meter air pistol with a first Olympic gold medal ahead of the likes of Beijing silver medallist Jin Jong-oh of South Korea and 2010 world champion Tomoyuki Matsuda of Japan.
Finals were also scheduled in the women's 48-kilogram class in weightlifting, two in judo, the men's team final in archery and women's individual foil in fencing.