Williams opened the night session on Arthur Ashe and proved too strong for Poland's Magda Linette, winning 6-4, 6-0.
"It's easy to play in", Williams said in a news conference afterwards.
But after French Open organizers ruled out a repeat of the black catsuit she wore in Paris for next year, all eyes were on what the 23-time grand slam singles champion would be wearing at Flushing Meadows.
Responding to a reporter who asked if there would be any birthday celebrations for her daughter, the 36-year-old had this to say: "Olympia doesn't celebrate birthdays". "Right now, I just feel like I'm on the road to getting better".
It's an experience you can only live in NY and it's one of the best feelings in the world. "The first set was tight. Once I got settled, I started doing what I'm trying to do in practice".
"The other day on a flight home Olympia insisted on running up and down the aisle and when I finally got her to sit still, she threw up all over me", she wrote, sharing a picture of the two of them together.
It was the 12th time Halep has lost in the opening round of a slam, and she said: 'I never play my best tennis here, even if I did quarter-finals, semi-finals.
Defending champion Sloane Stephens eased into the second round with a 6-1, 7-5 victory over Russian Evgeniya Rodina.
It would be the earliest matchup for the Williams siblings at a Grand Slam tournament in two decades: Their very first all-in-the-family showdown came in the second round of the 1998 Australian Open.