The 19-year-old from Yugoslavia played disinterested and distracted tennis, sometimes failing to run for shots or stabbing halfheartedly at a ball. She committed 29 unforced errors and lost her serve four times during the hour-long encounter.
"I didn't play well, didn't move so well," Dokic said. "I just had trouble staying in points because I made too many errors. It just wasn't good enough. Even when I had chances, I didn't take them. I didn't play the points smart."
Third seed Tommy Haas of Germany almost followed Dokic out the early exit door but rallied for a 7-6 (7-1), 3-6, 3-6, 6-4, 7-5 triumph over David Sanchez of Spain.
Haas' injured right arm manage to hold up through the three-hour, 23-minute match, but both players received medical treatment.
Fifth seed Tim Henman of Britain, who has an ailing right shoulder, also cruised into the second round. Henman routed Finnish qualifier Tuomas Ketola, 6-1, 6-1, 6-1, in 86 minutes.
Showing some of his old form, four-time champion Sampras cruised past Albert Portas of Spain, 6-1, 6-4, 6-4, in a first-round match.
Williams, the No. 1 seed, advanced to the third round with a 6-0, 6-1 victory over Russian teen Dinara Safina.
Dokic has had an excellent year, but injuries and off-court incidents appear to have weighed her down. The winner of two titles and a quarterfinalist at the French Open and Wimbledon, she performed well this summer while playing with a hamstring injury.
Dokic downplayed any health problems.
"It wasn't a factor the first day and it wasn't a factor today," she said. "I don't think too much this year. I took the week off last week. I just had one of those days where nothing was right. So it happened today."
Bovina, 19, advanced to the third round of a Grand Slam for the third time in her career. The Moscow native has blossomed since Joe Giuliano became her coach in March. Bovina reached the semifinals at Estoril and won her first WTA Tour title in Warsaw.
"I just found my rhythm from the beginning and I knew it was going to be a little bit windy outside," Bovina said. "I just tried to make a lot of balls, especially at the beginning of the match, make her play.
"I guess she just couldn't quite find her game today. She made a lot of errors today. I don't know what's the reason for her playing that way. Obviously, it's not my problem. I just try to play my game."
Haas developed tendinitis in his forearm muscles last week in Long Island after overcompensating for existing shoulder tendinitis, which he flared the previous week in Indianapolis.
The 24-year-old German's arm was ailing in the middle of Wednesday's match, when he fell behind two sets to one. But he was able to fight back to force a fifth set. After coming back from love-3 in the fifth, he twice double-faulted on match points, before taking the fifth in a tiebreaker.
"I got a little bit nervous (on the match points)," said Haas, who gave his postmatch interview standing because of cramps. "I couldn't push off that much. The first double-fault, you start to think. Just my legs wouldn't push off anymore. I was lucky to get through."
At No. 17, Sampras has his lowest Grand Slam seeding. If it were not for the extension of the seeds to include 32 players last year, Sampras would not be seeded here, something that has not happened since 1989.
The 31-year-old American has reached the final here the last two years but was beaten soundly by younger foes. He has not won a tournament since capturing his record 13th Grand Slam crown at Wimbledon in 2000, a span of 33 events.
"I'm still putting a lot of working into it, a lot of focus," he said. "It's been a pretty disappointing year. I have nothing to show for it. I can't dwell on that at the moment. I have to look at the future, not the past. I just have to believe in myself and hope I can do pretty well here."
He said he is hoping to draw inspiration from the New York fans.
"It's happened the last couple of years here when (I haven't) been quite as dominant and the support here in New York. Last year, I had a great run. The crowd helps. When you're feeling a little bit heavy in the legs, they kind of spur you on a little bit. It's always nice having that support."
Williams is trying to win her third consecutive Grand Slam and become the first woman to capture three major titles in the same year since 1997. But in Wednesday's match, she was looking to notch her first double-bagel victory (6-0, 6-0), something that sister Venus and Jennifer Capriati did on Tuesday.
"I did (try)," Serena Williams said. "But she played a good game. A few good games. Next time, maybe. I used to do it all the time in the juniors, but I haven't been able to do it yet."
Safina is the 16-year-old sister of men's second seed Marat Safin. She made her U.S. Open debut Monday with a straight-sets victory over Rita Grande. The Moscow native, who is coached by her mother Rouza Islanova, won her first career title this year at Sopot.
But playing the world No. 1 was another experience.
"I had chances to win, maybe, three games, and only got one," Safina said. "But she played really good. She wanted to win, 6-0, 6-0. She puts so much pressure and it's so hard. She hits the ball so close to the line and never plays two balls the same."
In other second-round women's matches, No. 8 Justine Henin of Belgium won over Zimbabwe's Cara Black, 6-3, 6-2; No. 12 Elena Dementieva of Russia was upset by Francesca Shiavone of Italy, 7-6 (9-7), 6-3; No. 15 Anastasia Myskina of Russia won over Denisa Chladkova of the Czech Republic, 3-6, 7-5, 6-3; No. 13 Silvia Farina Elia of Italy ousted Els Callens of Belgium, 6-2, 6-2; and No. 20 Daja Bedanova of the Czech Republic held off Elena Likhovtseva of Russia, 7-6 (7-2), 2-6, 6-3.