The 25-year-old eventually closed out the set and, despite going a break down in the first game of the decider, proved too strong for the 21-year-old Ukrainian, who was playing in the main draw of a Grand Slam for the first time.
Hours earlier, across the way at Louis Armstrong Stadium, Venus Williams did her part with another straight-set victory, eliminating 40th-ranked Camila Giorgi of Italy, 6-4, 7-5.
The 2000 and 2001 champion in NY will face Serena for a place in the last 16 if the six-time victor gets past Germany's Carina Witthoeft under the Arthur Ashe Stadium lights later in the day.
Serena Williams has responded to French Open officials criticizing her clothing at Roland Garros in the most Serena Williams way possible.
The last time the two have played this early in a Grand Slam tournament was in 1998 at the Australian Open in their first-ever meeting on the tour.
Venus said after her match, "we get to play".
Having opened up a double break lead, 36-year-old Serena was forced to save three break points in the seventh game before she wrapped up the opener on the Witthoeft serve.
"The more these incidents come out, that's a good thing", Asha Dahya, founder and editor of GirlTalkHQ, told ABC News.
The reason this match comes so early is that their rankings are not what they've been in the past.
The 21-year-old will play the victor of the match between Qiang Wang and Irina-Camelia Begu in the third round.
"You're beating it up now", the elder sister said. "So I think it's fine".
She faces Belarus' Victoria Azarenka next, after the former world number one beat Daria Gavrilova 6-1 6-2. "So it'll be a while before this even has to come up again", she said.
Estonia's Kaia Kanepi followed up her first round win over world number one Simona Halep by seeing off Jil Teichmann of Switzerland, 6-4, 6-3.
Serena Williams set up a third-round encounter with sister Venus as she defeated Germany's Carina Witthoeft in emphatic fashion at the US Open.
"If I would say my true feelings, it would be bleeped out, because it was ridiculous", said Azarenka. "Unsportsmanlike conduct.?? But the men can change shirts on court", tweeted Scottish tennis coach Judy Murray, who is the mother of professional tennis player Andy Murray.