Back from Beijing with her gold medal, Dementieva won the final four games. The fifth-seeded Russian was glad to win quickly and give her mind and body a break.
"It's very hard not to think about the Olympic Games," Dementieva said. "Very difficult to refocus. I mean, all my thinking is there in Beijing."
Former champions Lindsay Davenport and Svetlana Kuznetsova also opened with straight-sets victories. No. 23 Davenport beat Canada's Aleksandra Wozniak 6-4, 6-2, while third-seeded Kuznetsova rolled past Zhang Shuai of China 6-4, 6-2.
The final Grand Slam event of the season figured to be a scramble, especially on the women's side. Justine Henin retired and is not back to defend her title and Maria Sharapova is out with an injured shoulder.
Six different women have won the U.S. Open in the past seven years, and Dementieva is seeking her first major championship. But to her, the Olympic singles title counts.
"The biggest goal for the year was Beijing," she said. "In Russia, if you stop anyone in the street and ask what is a Grand Slam, I don't think many people can tell you. But everyone knows the Olympic Games. There is nothing bigger."
During a quick stopover in Moscow to see her mom, she found out how much the gold meant.
"People just come to me and say, 'Oh, I'm happy for you. You're always losing in the final. It's so great that you finally win something big,'" said Dementieva, who will next play France's Pauline Parmentier, a 6-3, 7-6 (2) winner over Marina Erakovic of New Zealand.
Dementieva put together a workmanlike win over Amanmuradova. Her opponent from Uzbekistan served for the second ahead 5-3, but Dementieva still had enough energy.
"I don't know what is best, to be a little bit tired but very comfortable and very positive or to be fresh and not play in the Olympic Games," she said.
At the ripe old age of 32, Davenport has no idea exactly how much longer she can continue competing, and that is exactly the way she likes it.
"Each time I play a Grand Slam I always think that, 'Oh, this could be my last time playing here,'" she said after reaching the second round of the U.S. Open.
"I've obviously learned that I have no idea what the future kind of holds and what will happen, and I don't make decisions for the future any more from this day that I'm living in," she said. "But I'm so excited to be back here. I didn't think I would be back playing. You never know how many more chances you'll get to be playing here."
The American, a three-time Grand Slam champion, thought her career was all but over when she went on a maternity break in September 2006.
However, she returned to action just three months after the birth of her son, Jagger, in June 2007 and enjoyed an astonishing run in which she won two of the three tournaments she entered last season.
This year has been more frustrating as she has spent more time in the physio's room than on a tennis court. A right knee injury meant she was able to contest only one singles match since April before arriving in New York.
Hence, while most competitors like talking up their chances at the majors, Davenport has adopted a more cautious approach.
"It's obviously been a battle this year and a battle that it's been hard to fight," said Davenport, who will next face Russia's Alisa Kleybanova, a 6-2, 7-5 winner over Carla Suarez Navarro of Spain.
"I really don't have any performance goals because I don't know really what will happen. My biggest thing is I feel like if I can stay healthy I give myself a chance to do well. I don't know what well kind of means anymore but I'm just shooting to play well, and today was a good step," she said.
As a working mother, Davenport admitted her priorities had also changed.
"Just to be on this journey with my son has been quite exciting and memorable and I have a good time with that," she said. "The kid has no idea if I've won or lost, he napped through my whole match today in the hotel. But for me and [husband] John, it's all about having him along with us every step of the way."
Second seed Jelena Jankovic underlined her title credentials by cruising into the second round with a commanding 6-3, 6-1 win over American teen Coco Vandeweghe on Monday.
The Serb, who briefly claimed top spot in the world rankings earlier this month, dominated with her crunching groundstrokes before wrapping up victory in an hour at Flushing Meadows.
Vandeweghe, 16, failed to make much of an impression in her first Grand Slam appearance despite a hard-hitting game, totaling 33 unforced errors in an evening match on the Arthur Ashe Stadium court.
"I was excited to go on court, play my match and get the job done," Jankovic, 23, said. "I was also quite nervous tonight, I don't know why. It was my first match and I was playing an opponent who I didn't know.
"All I knew, she was a junior and I only heard that she was 16 years old they said when they introduced her on the court. She was hitting the ball so hard, maybe harder than the top players," Jankovic said. "And it's always tough to play an opponent who doesn't have anything to lose, especially in the first round with the windy conditions out there.
"But I did as much as I needed to do to win the match," the Serb No. 2 added. "I am happy with my win and looking forward to the next round."
Jankovic is among the title favorites for the last Grand Slam event of the year.
She reached the semifinals at the Australian Open and Wimbledon earlier this season, successfully defended her title in Rome in May and is vying with compatriot Ana Ivanovic for the No. 1 ranking.
"To reach the No. 1 spot is amazing," said Jankovic, who
replaced Ivanovic at the head of the rankings on Aug. 11 before
slipping back to number two the following week.
"And it's something that will stay in my record, in my
biography, for the rest of my life. Nobody can take that away
"I'm only the 18th player to achieve that. It's a huge
achievement and I'm really proud to join a selection of great
champions. Of course I want to keep developing my game and keep
improving. In order to do that, the priority is to be healthy."
The 10th seed, whose only previous opening-round defeat was at Wimbledon in 2005, looked to be coasting toward victory when she romped through the opening set.
But the 21-year-old wilted under a barrage of withering groundstrokes from her left-handed opponent in the next two sets.
Chakvetadze flicked a forehand long on match point to surrender her title hopes after 1 hour, 45 minutes of seesaw action.
Other seeded players to advance were eighth-seeded Vera Zvonareva of Russia, who beat Barbora Zahlavova Strycova
of the Czech Republic 6-4, 6-3; No. 12 Marion Bartoli of France, who beat Galina Voskoboeva of Russia 6-2, 6-3; No. 14 Victoria Azarenka of Belarus, a 6-2, 6-1 winner over Klara Zakopalova of the Czech Republic; No. 15 Patty Schnyder of Switzerland, who needed three sets to beat Anastasia Pivovarova of Russia, 6-3, 3-6, 6-3; No. 25 Francesca Schiavone of Italy, a 7-5, 7-5 winner over Nuria Llagostera of Spain; No. 28 Katarina Srebotnik of Slovenia, a 3-6, 6-0, 6-3 winner over Belgian Yanina Wickmayer; No. 26 Anabel Medina Garrigues of Spain beat Bulgaria's Tsvetana Pironkova 6-4, 7-5;and 29th-seeded Austrian Sybille Bammer, who cruised past Aiko Nakamura of Japan 6-4, 6-2
In other action, Italy's Maria Elena Camerin rolled past Emilie Loit of France 6-0, 6-2; Aravane Rezai of France beat Asia Muhammad of the United States 6-2, 6-4; Italian Sara Errani beat Jelena Kostanic Tosic of Croatia 6-4,
6-2; Iveta Benesova of the Czech Republic rolled past Italian Karin Knapp 6-0, 6-3; Australian Yvonne Meusburger beat Lourdes Dominguez Lino of Spain 6-1, 6-2; Magdalena Rybarikova of Slovakia crushed Gisela Dulko of Argentina 6-4, 6-0; Tatiana Perebiynis of the Ukraine beat compatriot Mariya Koryttseva 6-1, 6-4; Romania's Sorana Cirstea held off Lucie Safarova of the Czech Republic 6-4, 4-6, 6-2; and Virginia Ruano Pascual of Spain rallied past Petra Kvitova of the Czech Republic 6-7 (3), 6-4, 6-2.
The Americans in action were ousted Monday. No. 21 Caroline Wozniacki of Denmark defeated Ahsha Rolle 6-2, 6-1. Vania King fell to Russian Anastasia Pavlyuchenkova 6-2, 4-6, 6-2; Anne Keothavong of Great Britain cruised past Alexa Glatch 6-2, 6-2; and Zheng Jie of China beat Shenay Perry 6-2, 6-3.
No. 1 Ivanovic and the Williams sisters were scheduled to begin Tuesday.
Information from The Associated Press and Reuters was used in this report.