Williams struggled with a back problem at the U.S. Open but said she felt better in her return to the court, breaking Bencic five times and losing her own serve only once in the first set.
"I was playing with some problems at the Open. It was difficult to serve, and that's a huge part of my game,'' Williams said. "But I have worked really hard to be able to be here, and I came planning to put some good serves in the box.
"I was happy with it today. Right now I'm going more for percentage than power, which is tough, because I really like hitting it hard.''
Bencic was playing her first tour match and said she had been excited when she saw the draw.
"It was a very great experience to play against Venus in my first WTA main draw,'' she said. "There were things I could have done better, but I'm happy how I did.''
Earlier, top-seeded Roberta Vinci of Italy beat an inconsistent Olga Govortsova of Belarus 6-0, 2-6, 6-0 to reach the second round. Govortsova won just six points on her serve in the first set, and nine in the third - but she converted all three of her break points in the middle set in a see-saw match.
Jelena Jankovic also advanced when China's Peng Shuai retired with a shoulder injury while the former top-ranked Serb was leading 3-0.
Second-seeded Julia Goerges of Germany easily beat Spain's Silvia Soler-Espinosa 6-2, 6-1, while Belgium's Kirsten Flipkens eliminated fifth-seeded Sabine Lisicki of Germany, 3-6, 6-3, 6-1.