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."
"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!"
The fifth seed showed the sort of ruthless precision that won her the French Open title this month. She broke Bacsinszky's serve five times on Thursday, forcing her Swiss opponent to scramble left and right to retrieve powerful groundstrokes.
Sharapova, the world's highest-earning sportswoman, moved with economical ease on Court One and has completed two rounds for the loss of only four games.
Two women tipped as outsiders for the title progressed on Thursday with big-serving American Madison Keys beating 31st seed Klara Koukalova 7-5 6-7(3) 6-2 and Canada's French Open semi-finalist Eugenie Bouchard too good for Silvia Soler Espinosa.
Results from the Wimbledon Women's Singles Round 2 matches on Thursday
Madison Keys (US) beat 31-Klara Koukalova (Czech Republic) 7-5 6-7(3) 6-2
Vera Zvonareva (Russia) beat Donna Vekic (Croatia) 6-4 6-4
5-Maria Sharapova (Russia) beat Timea Bacsinszky (Switzerland) 6-2 6-1
9-Angelique Kerber (Germany) beat Heather Watson (Britain) 6-2 5-7 6-1
13-Eugenie Bouchard (Canada) beat Silvia Soler Espinosa (Spain) 7-5 6-1
Alison Riske (US) beat Camila Giorgi (Italy) 7-5 6-2
20-Andrea Petkovic (Germany) beat Irina Begu (Romania) 6-4 3-6 6-1
19-Sabine Lisicki (Germany) beat Karolina Pliskova (Czech Republic) 6-3 7-5
Zarina Diyas (Kazakhstan) beat 15-Carla Suarez Navarro (Spain) 7-6(12) 5-7 6-2
24-Kirsten Flipkens (Belgium) beat Lourdes Dominguez Lino (Spain) 6-2 6-1
Yaroslava Shvedova (Kazakhstan) beat Kaia Kanepi (Estonia) 6-3 6-7(4) 6-2
11-Ana Ivanovic (Serbia) beat Zheng Jie (China) 6-4 6-0
25-Alize Cornet (France) beat Petra Cetkovska (Czech Republic) 6-4 5-7 6-3
1-Serena Williams (US) beat Chanelle Scheepers (South Africa) 6-1 6-1
- Sports & Recreation
- Timea Bacsinszky
- Maria Sharapova