All the worries over Serena Williams’s right shoulder and concerns about her difficult first-round opponent seemed to vanish in a little over an hour Tuesday, as Williams let the rest of the women’s field know that despite the alarms, she is in very good form.

The top-seeded Williams opened her 2016 United States Open campaign with a smooth 6-3, 6-3 win over No. 29 Ekaterina Makarova and moved a step closer to the title that eluded her a year ago. Also on Tuesday night, second-seeded Andy Murray defeated Lukas Rosol, 6-3, 6-2, 6-2.

Williams’s previous match at the U.S. Open was her surprising semifinal loss to Roberta Vinci in 2015, which prevented Williams from winning the Grand Slam.

“I had a great experience last year,” she said. “I was going for something that no one has done in a really long time. Yeah, it didn’t end up wonderful for me or the way I wanted it to end. But it was all I could do. If I could make the semis this year, I’d be excited about that. I need to at least do something.”

This year Williams is seeking her 23rd title in a major tournament, which would move her past Steffi Graf for the most in the Open era. She is also in pursuit of a record seventh U.S. Open title, which would break a tie with Chris Evert.The smiles and hugs that were exchanged by members of her support team after the match, including her coach Patrick Mouratoglou, suggest Williams is ready for the challenge.

Wearing compression sleeves on both arms, Williams moved well across the court.

Her serve was more than strong enough to dismiss most of the concerns about the shoulder injury that prompted her to withdraw from the Western & Southern Open in Cincinnati this month.

Williams said the key, though, would be how she felt Wednesday.

Her average first-serve speed was 108 miles per hour, and she touched 121 m.p.h. on her fastest delivery. She served 12 aces, eight in the first set, to overwhelm Makarova in 62 minutes.

Makarova beat Williams at the Australian Open in 2012, but there was little to resemble that match on Tuesday, which was a good day over all for the Williams family.

Before Serena Williams took the court, her sister Venus, seeded sixth, defeated Kateryna Kozlova of Ukraine, 6-2, 5-7, 6-4, to improve her record in the first-round of the Open to 18-0.Venus Williams said she knew nothing about her opponent before the match. She said mistakes led to her dropping the second set.

“I definitely had a lot more errors than I wanted,” she said. “If I could cut those in half, it’s definitely a different story.”

She made 63 unforced errors to 39 for Kozlova.

Venus Williams was playing in the main draw of a record 72nd Grand Slam event, breaking a tie with Amy Frazier for the most in the Open era.

She reflected back on her first final here, in 1997, which she lost to Martina Hingis, and wondered if her younger sister could have won.

Perhaps Serena could have. But the more pertinent question today is whether Serena Williams can win a match a week from Saturday, when the final is scheduled, even if her shoulder is sore.

“I wouldn’t bet against her,” Venus Williams said. “Honestly, I wouldn’t want to do that.”