Defending men's champion Novak Djokovic advanced to the fourth round of a Grand Slam for the 25th consecutive time in easier fashion, with 15 service aces and 38 winners to beat Bernad Tomic 6-3, 6-3, 6-3. French Open champion Stan Wawrinka also breezed to a 6-4, 6-3, 6-4 win over Fernando Verdasco.
"I served well. It's not easy to win against Bernard in straight sets. I am pleased with the way I'm playing, I'm very close to where I want to be," Djokovic said.
Williams was down two breaks in the third set before she staged an impressive rally against the young Watson, winning four straight games and then producing two late breaks to salvage the victory. She'll next face sister Venus Williams for the sixth time at Wimbledon and the 26th time in their careers. Serena has a 14-11 record in head-to-head meetings and is 3-2 at Wimbledon.
Venus had an easier time in the third round, defeating Aleksandra Krunic 6-3, 6-2. The sisters will play Monday.
Maria Sharapova also advanced at the All England Club, dispatching Romanian Irina-Camelia Begu 6-4, 6-3.
"There is only one champion in the end and the one who raises their game is the champion," said Sharapova, who won the ladies singles in 2004.
There was one upset on the men's side. Nick Kyrgios upended No. 7 Milos Raonic 5-7, 7-5, 7-6, 6-3.
Saturday's order of play:
Samuel Groth vs. No. 2 Roger Federer
No. 5 Caroline Wozniacki vs. Camilia Giorgi
No. 9 Marin Cilic vs. No. 17 John Isner (completion of suspended match)
James Ward vs. Vasek Pospisil
No. 20 Garbine Muguruza vs. No. 10 Angelique Kerber
No. 15 Timea Bacsinszky vs. No. 18 Sabine Lisicki
No. 22 Viktor Troicki vs. Dustin Brown
No. 13 Jo-Wilfried Tsonga vs. No. 23 Ivo Karlovic
Nikoloz Basilashvili vs. Roberto Bautista Agut
No. 21 Madison Keys vs. Tatjana Maria
Kristyna Pliskova vs. Monica Niculescu
No. 13 Agnieszka Radwanska vs. Casey Dellacqua
Magdalena Rybarikova vs. Olga Govortsova