With the victory, Williams becomes the oldest Wimbledon quarterfinalist since Martina Navratilova in 1994. The surface benefits her booming ground strokes, one of the strengths that Coco Vandeweghe of the USA couldn't blunt in yesterday's 6-3, 6-3 defeat.
Williams will next face Britain's Johanna Konta, who lost the first set before rallying to beat second-seeded Simona Halep 6-7 (2), 7-6 (5), 6-4 on Thursday.
Williams, however, knocked the stuffing out of the first Latvian Grand Slam victor with her first serve and then preyed mercilessly on Ostapenko's timid second serve.
She made it that far at Wimbledon a year ago, too, before losing, and got to the final at the Australian Open in January, when she was beaten by her younger sister, Serena. "I know she acts like this all the time".
Contesting Wimbledon for the 20th time, Williams advanced to the last four for the 10th time with a 6-3 7-5 victory over erratic Ostapenko.
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However, the USA ambassador's Spaso House residence and the Anglo-American School in St Petersburg would not be affected. Russian Federation says President Trump presented "no plan to resolve the crisis" when the issue was raised in Hamburg.
The men traditionally have Tuesday off at Wimbledon, but Rafael Nadal's five-set loss to Gilles Muller on Monday forced Djokovic's match to be pushed back a day.
Kuznetsova enjoyed strong starts in both sets but failed to capitalise and it was Muguruza's superior serving and movement that proved decisive on Court One.
That would be Slovak Magdalena Rybarikova, Spanish-Venezuelan Garbine Muguruza and the one, the only, the eternal Venus Williams, all of whom on Tuesday joined British No. 1 Johanna Konta as survivalists into the Wimbledon semifinals.
"Muguruza impressed me a lot today, I am not the favourite again but let's see". "But I'm still managing to play, which is the most important thing".
"I feel quite capable, to be honest, and powerful", she said. Venus made her jittery to make it 40-30 at one point but the Latvian held on to win her first game.
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An inquiry will take place into the deaths of thousands of people who were given contaminated blood during the 1980s . The spokesman said the decision to hold an investigation had been prompted by new evidence.
Ostapenko can make unforced errors but this wasn't an erratic performance, evidenced by her final tally of 20 winners and 18 unforced errors.
The sisters have won seven of the last 10 titles between them at the All England Club, with Serena claiming five and Venus two. The Russian won the first set 7-5 and was trailing 0-1 in the second when she retired after 39-minutes of play. Halep made it to the finals of the French Open, but fell short of her first Grand Slam win when she lost to the unseeded Ostapenko.
There was not so much as a break point on offer for Ostapenko in that opening set and when a glimmer of light appeared, she could not walk towards it. "I did that and feel fortunate to have taken a few of them".
If she wins Wimbledon it will be the first grass-court title of her career, coming just two weeks after she feared her participation in the tournament might be ruined by a back injury suffered in the Eastbourne warm-up event.
Venus added: "When you're out there, all you're thinking about, especially at least on my side, all I can control is myself. For me, myself, I'm happy to be on any court". "I'd like to think that I can continue to rely on that as the matches continue".
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If they do not get that far the remaining matches of the ban will be served in Mexico's subsequent official internationals. Osorio is now with his team in San Diego as they prepare for the tournament.