The American seems to be starting all her matches this tournament slowly, but so far she is finishing strongly enough to progress.
Williams revealed after the match that her comeback victory was inspired by sister Venus.
She said: "She kept hitting winners and there wasn't anything I could do. But when in doubt, just keep running. That's what Venus always told me."
Serena faces No. 24 Garbine Muguruza after Muguruza defeated Timea Bacsinszky 6-3, 4-6, 6-0. Muguruza defeated Williams in the French Open last year, so she will need to up her game in order to progress to the quarter finals.
Venus also made a comeback victory to book her place in the fourth round, the first time she has gone this far in a Grand Slam since Wimbledon in 2011.