Pushed to the absolute limit,
Down 3-0 and 5-4 in the third set, twice within two points of defeat,
Next up for the five-time champion: a fourth-round matchup with sister Venus.
Top-ranked Serena looked on the ropes after losing six games in a row and going two breaks down in the third set. But, just as she has done so many times before, she refused to lose.
Williams ran off four games in a row as she battled back, and broke Watson in the 12th game to win on her third match point and extend her Grand Slam winning streak to 24 matches.
"I've had some tough losses, but that was probably my toughest match I've played [on Centre Court]," Williams said. "Heather playing in front of her home crowd … I think she played unbelievable. She should have won the match at this point, she was up two breaks and she just really gave her all."
The 59th-ranked Watson, lifted throughout the match by a raucous partisan crowd, played the match of her life but fell short of becoming the first British woman to beat a No. 1 since Sue Barker defeated Chris Evert in Boston in 1979.
"It was super, super close, and that's what hurts the most," Watson said.
Venus Williams, also a five-time champion, made it to the fourth round for the first time since 2011 by beating Aleksandra Krunic of Serbia 6-3, 6-2.
That sets up the 26th career meeting between the sisters — and the first at a Grand Slam since Serena won in the 2009 Wimbledon final. Overall, Serena leads 14-11.
"She's in better form than I am," Serena said of her older sister, "so I think she has a little bit of an advantage going into that match. But at least one of us will be in the quarterfinals, so that'll be good."