Sun was fastest in 1 minute, 46.24 seconds coming off his victory in the 400 free on Saturday.
"I'll try to do my best, but the 200 freestyle is not my best event," he said. "It's more difficult for me compared to the 400 metres or the 1,500 metres."
Lochte was second at 1:46.45, having won the 400 individual medley on the first night of Olympic swimming.
"I didn't get to bed until like 2 a.m. so I'm a little tired, but it was a prelims swim, so I'm not too worried about it," said Lochte, who was out celebrating with his family.
Yannick Agnel of France was third at 1:46.60. Also advancing was Park Tae-hwan of South Korea, who finished second behind Sun in the 400 IM after initially being disqualified in the prelims and then reinstated. Park was fifth-fastest at 1:46.79.
Among the top 16 moving on to the evening semifinals were Robbie Renwick of Britain (sixth) and Kenrick Monk of Australia (seventh).
Ricky Berens of the United States was eighth in his first-ever individual Olympic event. Paul Biedermann of Germany, the world-record holder, was 10th in 1:47.27 after failing to advance out of the 400 free prelims on Saturday.
Emily Seebohm of Australia qualified fastest in the 100 backstroke with an Olympic-record time of 58.23 seconds. She lowered the old mark of 58.77 set by Kirsty Coventry of Zimbabwe four years ago in Beijing.
"I saw that I was ahead of the world record and I was just like, 'Don't get over your head. Just keep going and just go as hard as you can,'" Seebohm said. "All I wanted to do this morning was to make it through. My goal was just to keep moving forward and now maybe the world record in the final, who knows?"
Missy Franklin, the 17-year-old American competing in her first Olympics, was second-quickest in 59.37. She earned a bronze medal as part of the U.S. 4x100 freestyle relay on the first night of swimming Saturday, but was still nervous for her first individual event.
"Oh my gosh. You can't take any chances here," Franklin said. "You have to get out there and do the best that you can. I know I can do faster than I did in prelims."
Franklin is set to swim seven events in London.
Belinda Hocking of Australia was third in 59.61.
Ten of the 16 women qualifying for the evening semifinals swam under 1 minute.
Anastasia Zueva of Russia, the silver medallist at last year's world championships, was fifth. Current world champion Zhao Jing of China was ninth.
A pair of British swimmers had the home fans cheering loudly. Georgia Davies was sixth, while world-record holder Gemma Spofforth moved on in 12th.
Rachel Bootsma, the other American teenager in the event, was 11th.
"I wasn't expecting to swim like that, but I guess I was nervous," she said. "At trials and finals, I went out too fast. I was a little nervous about doing that here. I think I held back a little too much."
Coventry, the silver medallist in the last two Olympics, barely advanced, grabbing the next-to-last spot in 1:00.24.
"I've been up and down coming into the competition with my knee and then pneumonia, so I'm just excited to be here," Coventry said. "I'm just enjoying my fourth Olympics and I'll see what I can do."
Two-time defending champion Natalie Coughlin failed to qualify for her signature event at the U.S. trials last month.
Ruta Meilutyte, a 15-year-old from Lithuania, topped the 100 breaststroke prelims in 1:05.56. It was the fastest time in the world this year and eighth-fastest ever in the event.
"I didn't expect it at all," said Meilutyte, who is trying to win her country's first Olympic swimming medal. "I am in shock."
Rebecca Soni, the 2008 silver medallist , was second at 1:05.75.
"It's great to see someone swim faster than they thought they could, to see that joy," Soni said of Meilutyte. "It rubs off on the rest of us too. It inspires me to push a little bit harder."
Yuliya Efimova of Russia, Soni's California training partner, was third at 1:06.51. Breeja Larson of the U.S. was fourth at 1:06.58 in her Olympic debut.
Defending Olympic champion Leisel Jones of Australia moved on in fifth at 1:06.98. Jones has medaled in the event in three previous Olympics.
Unflattering photos of Jones appeared in Australian newspapers before the Olympics and she said the critical comments were hurtful.
"It has really motivated me. I am one of those people you put me under presure and I show what I can do," she said. "I did one of my best sessions ever after reading those comments."
In the men's 100 back, Matt Grevers of the United States led the way in 52.92. He's in pursuit of the gold after earning a silver four years ago behind countryman Aaron Peirsol, who retired after winning two Olympic titles in the event.
Feiyi Cheng of China was second at 53.22. Grevers' teammate, Nick Thoman, was third at 53.48. Among others advancing to the semifinals were Camille Lacourt of France (fourth), Ryosuke Irie of Japan (fifth) and Helge Meeuw of Germany (seventh).