Williams had her service broken in the opening game before settling in. She needed just 68 minutes to advance, firing seven aces and taking advantage of eight double-faults by Scheepers.
The former top-ranked Williams said frequent long rallies provided a tough opening workout for her, and she looked forward to playing young Serbian Bojana Jovanovski in the second round.
“That was definitely not easy, I think she (Scheepers) played really well,” Williams said. “I didn’t expect that.”
In other matches, former No. 1-ranked Ana Ivanovic beat Tamira Paszek of Austria 6-3, 6-3 and American qualifier Vania King beat Melinda Czink of Hungary 6-3, 6-4.
Sam Stosur, who beat Williams for the U.S. Open title, plays her opening match at Pat Rafter Arena on Monday night.
Top-seeded Andy Murray plays his opening men’s match on Tuesday. Second-seeded Gilles Simon of France advanced with a 6-3, 6-4 win over American Ryan Sweeting on Monday.
Denis Istoman of Uzbekistan also went through to the second round when Florian Mayer of Germany retired with a groin injury while trailing 7-6 (5), 2-3, and eighth-seeded Bernard Tomic of Australia beat Julien Benneteau of France 6-2, 4-6, 7-5.
Former Australian Open finalist Marcos Baghdatis had a night match against American Ryan Harrison.
Ivanovic will play Australian Open defending champion Kim Clijsters in the second round, one of the toughest rivals either player has faced so early in a tournament.
The last time the two players met, former French Open champion Ivanovic blew five match points at Miami last March. Ivanovic had three break points when leading 5-1 in the deciding set before Clijsters came back to win 7-6 (4), 3-6, 7-6 (5) and improve her career record with Ivanovic to 4-0.
“Last time it was a hard one for me,” Ivanovic said Monday. “It would be nice to convert a match point. I will go out there and test myself, push and see how far away I am from the top players.”
Ivanovic finished 2011 outside the top 20 for just the second time since 2004 after a series of injuries.
“Hopefully this time I can take it a step further,” Ivanovic said.
Clijsters has played just one match since returning from an abdominal injury that prevented her from defending her U.S. Open title, a 6-1, 6-4 first-round win here over Romania’s Simona Halep on Sunday.
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