Serena Williams rides serve to first-round win over Ekaterina Makarova

— -- NEW YORK -- If this is how Serena Williams serves when she can't practice properly because her right shoulder is sore, watch out when she's 100 percent healthy.

A year after falling two wins short of a calendar-year Grand Slam by bowing out in the US Open semifinals, Williams showed zero signs of shoulder trouble on Tuesday night as she began her bid for a record-breaking 23rd major title.

She hit 12 aces and reached 121 mph on her powerful serve during a 6-3, 6-3 victory over Ekaterina Makarova, a potentially tricky first-round opponent at Flushing Meadows.

"I was pleased with my serve, because I haven't been hitting a lot of serves at all,'' the 34-year-old Williams said. "In practice, none of them were going in, so I was definitely excited about that."

Since equaling Steffi Graf's mark for most Grand Slam singles trophies in the Open era, which dates to 1968, by earning No. 22 at Wimbledon in July, the No. 1-ranked Williams had entered only one event -- the Rio de Janeiro Olympics, where she was upset in the third round. She cited a sore shoulder in withdrawing from a hard-court tournament a week later.

She looked perfectly fine against Makarova, a two-time Grand Slam semifinalist who is ranked 29th. Makarova beat Williams in straight sets at the 2012 Australian Open.

"I knew today I needed to be focused, because I've played her," Williams said of Makarova. "She's gotten to the semifinals. She goes deep in majors. She knows how to play big matches on big courts. She's not intimidated. I knew I had to really come out today. It was my only option, really."

Well, consider that done.

Wearing black sleeves on each arm -- she called the accessories "definitely functional,'' because they "keep my muscles warm" -- Williams averaged 108 mph on first serves and won 17 of the first 20 points she served, 36 of 46 overall, never appearing to be the least bit bothered by anything.

And she even figured that maybe the time she couldn't spend serving during training sessions paid off, in a way, because she was forced to address other aspects of her game, including footwork.

"I couldn't hit any balls. I wanted to stay fit, so ... I guess that kind of helped me out a little bit," she said.

In 2015, Williams arrived at the US Open having won four consecutive major titles for a self-styled "Serena Slam." But had she also won the championship in New York, she would have made it 4-for-4 within a single season, something no one had done since Graf in 1988.

But that pursuit ended with a surprising semifinal loss to Roberta Vinci of Italy.

Later, Williams acknowledged what was at stake had been a burden.

Williams was asked Tuesday whether this edition of the US Open might be a more pleasant experience than a year ago, without the same sort of history on the line.

"I had a great experience last year. I was going for something that no one has done in a really long time," she replied. "Yeah, it didn't end out wonderful for me, or the way I wanted it to end, but it was all I could do. That's all I could do. If I could make the semis this year, I'd be excited about that."

Meanwhile, her sister? Venus Williams needed three sets to win her 18th first-round match at the US Open.

She defeated Kateryna Kozlova of Ukraine 6-2, 5-7, 6-4, despite 63 unforced errors, and improved to 18-0 in the Open's first round. Only Chris Evert (19-0) has a better record in the first round in the Open era, according to ESPN Stats & Information research.?

She led 5-2 in the third set, but the 22-year-old Kozlova pushed her to the limit in the 2-hour, 42-minute match.

"It was great to be challenged and to be pushed," said the 36-year-old Venus Williams, a two-time US Open champion, "because I had to get in those situations that you know you're going to face in the tournament."

She next faces? Julia Goerges, who defeated Yanina Wickmayer 6-3, 6-2.

Also on the women's side,? Simona Halep gave herself "less than nine" for her quick work against Kirsten Flipkens.

The Romanian was ahead 6-0, 5-0, with countrywoman Nadia Comaneci cheering her on. Comaneci was the first gymnast to score a perfect 10 at the 1976 Montreal Olympics.

Halep, the fifth seed, was unable to complete the "double bagel," however, as she wound up winning 6-0, 6-2.

Halep said she wasn't perfect, but she was pleased with her play against the Belgian. She got 69 percent of her first serves in and won 12 of 15 points at the net.

Halep, who reached the semifinals of the US Open last year, will next face Lucie Safarova, a 6-4, 6-4 winner over Daria Gavrilova.

In other matches,? Ana Ivanovic?tumbled out of the US Open in the first round for the second straight year after a 7-6 (4), 6-1 loss to Denisa Allertova of the Czech Republic.

A former No. 1 player who has slipped to 31st in the rankings, Ivanovic was serving for the first set at 6-5 but struggled with her serve and faltered in the tiebreaker. The 2008 French Open champion finished with seven double faults and 41 unforced errors.

At the US Open, Ivanovic has reached the fourth round or better five times, including a career-best quarterfinal run in 2012.

Meanwhile, 2011 US Open champion? Samantha Stosur?advanced with a 7-5, 6-7 (4), 6-1 win over Camila Giorgi, who had an ace to win the second-set tiebreaker.

Stosur, however, streaked out to a 4-0 lead in the deciding set and next will face Zhang Shuai, who defeated Ellen Perez 6-1, 6-1.

The Associated Press contributed to this report.