Italy's Camila Giorgi swept aside Ekaterina Makarova of Russian Federation 6-3 6-4.
Williams responded by raising the intensity level and began striking the ball with ferocious power to break Giorgi's serve for the first time on her way to levelling the match.
Williams, a seven-time Wimbledon champion, was in danger of a stunning exit after world No 52 Giorgi became the first player in this year's tournament to take a set off the former world No 1.
But the third set was all Williams, and she recorded six of her seven aces - making it clear she's moved well past the pectoral injury that forced her to withdraw ahead of the fourth round in Paris - and seemed to be in control throughout.
Serena Williams loses the first set, but recovers to defeat Camila Giorgi and continue her quest for an eighth Wimbledon title. Coming into the tournament seeded 25, Williams has returned to form in spectacular fashion. She was the lone top-10 women's seed still around at this upset-filled tournament, and now she's also gone. Sure, there weren't a lot of long points, so maybe that's why I wasn't out of breath.
Gorges, 29, says it is an "honour" to share the court with Williams and that it is a reward for her decision three years ago to "start from zero" by changing her coach and physio and moving from the north to the south of Germany.
Pliskova winced as she struggled with what appeared to be a thigh problem and Bertens dominated a tie-break to march into the last eight, unleashing ferocious forehand winners before finishing it off with an overhead volley that clipped the line.
Thousands take to London streets to protest Trump
This is not to say Trump owes May an apology for criticizing her in the British press and praising her rival Boris Johnson . Trump has insisted the US-UK relationship is "the highest level of special". "I think you're losing your culture".
Goerges admitted it had been tough playing her close friend and occasional doubles partner on tour.
Shrieking and clenching her fists after every key point that went her way, Serena let out a gutteral "C'mon" once she wrapped up the set.
Serena Williams will face Julia Goerges in the semi-final of the women's bracket at Wimbledon 2018 on Thursday, the same day Angelique Kerber will meet Jelena Ostapenko in the last four. "It's a great opportunity for me to meet her at that stage".
Although All England Club chief executive Richard Lewis said there has been no approach from the White House over a possible visit, both players were asked about it following their victories. So I think it's a great week.
The highest seed left in the draw is Görges global teammate, Angelique Kerber.
Williams, a four-time Olympic gold medalist, is seeking her 24th Grand Slam title, which would tie Margaret Court for first on the all-time list.
In the upcoming round, Ostapenko will play Dominika Cibulkova of Slovakia, world No 33, who eliminated Taiwan's Hsieh Su-wei 6-4, 6-1.