The American top seed was first up on Court One on Thursday, having had to wait until 9pm the previous evening to clinch a three-set win with sister Venus, but looked fresh and eager to make short work of 94th-ranked Scheepers.
"I didn't sleep well yesterday. But I think I was just ready for my match," she told reporters after confirming she had suffered no ill-effects from the doubles tussle, during which she also took a tumble into a courtside spectator.
"(I) had some lovely gent who was able to break my fall," she joked.
Having dropped only three games in the previous round, Serena was even more convincing as she overpowered Scheepers, sending down eight aces and hitting 26 winners as she wrapped up proceedings in only 49 minutes.
The world No.1, who went out at this stage of last month's French Open, next faces Alize Cornet, who has already beaten the American this year.
The French 25th seed defeated Petra Cotkovska 6-4 5-7 6-3 to set up what Serena expects to be a more challenging test than Thursday's romp.
"Well, Cornet, she does everything good. That's why she was able to get a good win off of me," Serena said when asked about the imminent rematch.
"She never gives up, she's a big fighter ... But I'm ready. It's time for me to step up my game and do what I know I can do and do what I'm best at."
First, however, she will put her feet up in front of the TV to watch the U.S. soccer team in Thursday's World Cup clash with Germany in Brazil.
"Once I get out of here I'm going to go home and, you know, sit down on the couch and just get to watch. Go USA!"
(Editing by Pritha Sarkar and Martyn Herman)
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