The tournament opened Monday, with Williams winning her evening match 6-4, 6-0 over Poland's Magda Linette at the USTA Billie Jean King National Tennis Center in New York. Her next match is on Wednesday against Carina Witthoft in the round of 64.
"It's not easy to get to any point in my career," Williams told reporters. "The highs have been great, the lows have been, you know, like your normal lows. That's kind of how it is. You have to get through all those moments to live the next."
Halep was eliminated 6-2, 6-4 by Estonia's Kaiai Kanepi. No 3. Sloane Stephens also won in straight sets, beating Evgeniya Rodina 6-1, 7-5. No. 2 Caroline Wozniacki, No. 4 Angelique Kerber and No. 5 Petra Kvitova play in their round of 128 matches on Tuesday.
On the men's side, No. 1 Rafael Nadal won after David Ferrer retired. No. 3 Juan Martin del Potro beat Donald Young 6-0, 6-3, 6-4. No. 5 Kevin Anderson beat American Ryan Harrison in five sets and Andy Murray beat James Duckworth in four sets in his return to the Grand Slam stage.
Williams is a six-time champion at the U.S. Open, with her last Grand Slam coming in 2014 in New York.
Stephens and Nadal are the defending singles champions of the tournament.