Venus Williams hits a forehand against Oceane Dodin on Wedensday at the U.S. Open. (Geoff Burke/Usa Today Sports)

Amid all the talk of injured men’s players and the hullabaloo over Maria Sharapova reappearing in a Grand Slam, you could be forgiven for having overlooked ninth-seeded Venus Williams lurking there in the U.S. Open draw.

But in a prime-time slot in Arthur Ashe Stadium on Wednesday night, Williams reminded everyone of her presence. She beat the French 20-year-old Oceane Dodin, 7-5, 6-4, to advance to the third round, where she will meet Maria Sakkari of Greece.

Performing in front of a sold-out crowd of 23,771, Williams was more businesslike in her second match of the tournament than the first.

After fighting to earn a three-set victory Monday, Williams marched through the big-hitting Dodin, closing the match with a service break at love. She sealed the win by ripping a forehand return down the line, just out of the Frenchwoman’s reach, then gave the crowd her signature twirl at the net.

She hit 32 winners to 14 unforced errors, served six aces and had no reason to raise her grunts of effort anywhere near her top decibel.

It was the second main draw appearance in New York for Dodin, ranked No. 48 in the world, and just the ninth of her career. She has never been past the third round in a major.

“I played two big servers in both rounds,” Williams said. “When you get your opportunities, you do have to close on them, then sometimes they don’t come back. Today, by the stats, the match was super clean. . . . I feel like each round is a time to improve.”

Her performance Wednesday was a reminder that Williams is capable of making a deep run in a wide open women’s draw and extend her resurgent 2017 into the final major of the year.

Williams, 37, reached the final at Wimbledon and the Australian Open, which was her first appearance in a Grand Slam final since 2009. She lost to her sister, Serena, but the championship marked the beginning of a year in which tennis rewound the clock in terms of who occupied the top spots.

She arrived in New York after a fine hard-court swing leading up to the U.S. Open in which she made the fourth round in Toronto and exited in the second round in Cincinnati.

An eighth career Grand Slam title here would be another testament to her longevity.

Williams is seeking her third U.S. Open trophy — her first since she won two back-to-back in 2000 and 2001 — and her 50th career title overall. This is her 19th appearance in the major, the most of all active players on tour, and her 76th appearance in the main draw of a Grand Slam, the record in the Open Era.

Still she remains somewhat under the radar in these early rounds, even with her small chance of taking the No. 1 ranking from Karolina Pliskova at the end of the tournament.

A little less off-court spotlight suits the near-unflappable Williams just as much as when attention from the media is its most intense, though it does provide a stark contrast to Wimbledon. There, Williams spent an emotional two weeks navigating questions about her involvement in a fatal South Florida car accident in early June (she would later be cleared of wrongdoing). The controversy lasted nearly all the way until the final, which she lost to Garbine Muguruza.

(The Spanish champion, another title-contender in New York, had to wait to play her second-round match until around 10 p.m. Wednesday when a court was finally free. Tuesday’s rainout put 87 matches on the schedule in a single day.)

In New York, Williams resumed not knowing, or caring about, what was said about her in the press.

“For me, I’m just going on the court, practicing, preparing, and recovering and playing the match,” Williams said. “I’m not out there reading press, watching TV or trying to see who said I was going to win. At the end of the day there’s people who are talking about the winning and there are people who are actually playing the matches. I need to play the match.”