Muguruza, seeded 14th, saved a tricky break point on her second service game - the only one she faced all match - but roared back to break to love en route to taking the first set.
"Now she played a brilliant game and match".
Kuznetsova didn't put enough pressure in her return games, she saved a set point with a massive forehand victor but the world number 15, her lowest rank in two years, sealed the set at the second chance.
Making her Centre Court debut Ostapenko was a little more subdued than normal but received a glowing report from the veteran of 75 grand slam campaigns. Venus will now serve to stay in the set.
Ostapenko makes a stunning comeback into the set and makes it 4-4. Her 2015 semifinal, she added, "seems far away from that".
Australia showcased Serena's unwavering talent and Venus' unerring desire for competition - a zest for the fight that is showing itself once again. "I think it's very hard for them to understand my position", she said.
Venus is now doing it easily out there as she blanks Ostanpenko in her own serve.
Williams gained the upper hand in the second set, too, but a double fault allowed Ostapenko to level at 3-3. The American in pole position to clinch the match now.
Key stat: Rarely seen on today's circuit, Rybarikova's game - with her forward moving serve and delicately placed volleying - lends itself to the serve-and-volley approach.
What a way to win the first game of the second set.
SET: That's it then!
She has not won a Grand Slam title since winning Wimbledon in 2008.
Facing each other across the net for the first time, the oldest and youngest players left in the singles draw slugged it out in a quickfire contest that was littered with as many unforced errors as clean winners.
Against Venus, she will probably need to be more ruthless than she was in finishing off Svitolina.
Williams' press conference following her first-round win had to be stopped temporarily when she wept fielding questions about the vehicle accident. Ostapenko needs to get back into the match quickly. The former junior Wimbledon champion regards grass as her best surface, and relished the chance of the biggest opponent on the biggest stage.
That was not the start of a comeback, however, and Ostapenko wrapped up the first set with another break before racing into a 5-2 lead in the second.
Federer into Wimbledon fourth round for 15th time
However, just like the Swiss, 13th seeded Dimitrov has yet to drop a set at this year's Wimbledon and was a semi-finalist in 2014. It looks set to be a frustrating day at Wimbledon . "I expect that every time I have played him he has become better".
Thousands flee wildfires in California, Canada
Eric Peterson, Santa Barbara County fire chief, said unsafe conditions meant the campers could not be taken out right away. No major injuries have been reported in California's Alamo Fire , according to Santa Barbara County spokesman Gina DePinto.
Yankees' Aaron Judge wins home-run derby
Judge has created an incredible buzz around the majors and that should continue in his initial MLB Home Run Derby appearance. And with Judge tipping the scales more than any Home Run Derby victor in history, he might be the one to bring home the win.
Amazon Echo Will Cost £80 On Amazon Prime Day
For its debut in India, Amazon has tied-up with multiple brands across categories to bring exclusive offers to its Prime members . Also, after buying you will get $5 credit as usual which you can use to buy other stuff on Amazon.com within limited time.