With the Ashe crowd behind her in the final set tiebreak, Williams willed her way to a 5-1 lead and when Kvitova sailed a return wide for 6-2, the American sealed the victory.
Muguruza remains ahead in a three-woman fight for world number one after the US Open but can be overtaken by Czech current number one Karolina Pliskova if she makes the final or Ukraine fourth seed Elina Svitolina if she reaches the semi-finals.
The pair completed half of what could be an American clean sweep of the semi-finals, with Coco Vandeweghe and Madison Keys playing their matches on Wednesday.
Williams, who improved to 2-4 all-time against the Czech 13th seed, is to return to the world top five for the first time since January 2011, a span that saw her diagnosed with energy-sapping Sjogren syndrome. "That would be huge".
Venus, the 37-year-old ninth seed, who has already played two Grand Slam finals this season, blossomed under pressure in a nail-biting third set to remain on course for her first major title since she won Wimbledon in 2008. A loose Williams game early in the second offered Kvitova the lifeline she needed and she clawed back to take the second set.
I try to tell myself to enjoy the competition, enjoy the battle and I think I was able to do that. Her track record at the major tournament also includes titles in both doubles and mixed doubles.
"It's great for African-American women", Stephens said.
In the men's draw, Spaniard Pablo Carreno Busta reached his first grand slam singles semi-final when he swatted aside Argentine Diego Schwartzman 6-4 6-4 6-2 in just under two hours. "It was pretty close but pretty far, as well". Venus was just a bit better in the final set tiebreaker to book her spot in the final four.
A protective splint was required for eight weeks but therapy began immediately, at first simply gripping a glass or a soft ball, then progressing to holding a tennis racquet, but only for a minute at a time.
"So probably my mind was just there, thinking about it. If you're down, you keep going", Williams said.
"If someone would have told me when I started at Wimbledon that I'd be in the semifinals, I would have said they're insane", Stevens said.
The 2000 and 2001 U.S. Open champion continued to serve nearly perfectly and pocketed the opening set when Kvitova, who hit 16 unforced errors, returned long.
A win on Tuesday night could provide her second-ever trip to a semifinal at a Grand Slam. "I don't get nervous or tight because I have to defend points or because I won a tournament previous year". She added: "I'm glad that I am still able to compete at a high level against the top players, which I hope will give me some confidence to work hard again and continue to play well, to know that it's still there somewhere". "I knew if I just stick with it and stayed in every point I'd have my opportunity and I did". "I wasn't trusting in it because I was kind of afraid because I didn't want to fall". Just happy with where I'm at.
Former Virginia Tech coach Frank Beamer, who will help with the coin toss, spoke with NCAA.com on the renewal of the rivalry. Even with the quarterbacks, the start was all about defense, as Virginia Tech took a narrow 10-7 lead into the half.
So the question is whether North Korea will put some checks on itself as it seeks to expand its weapons tests in the Pacific. Tensions between America, North Korea, and the hermit state's regional neighbors have been rising for months.
Episode one pulled in 6.5 million viewers, more than double the number Channel 4 had previously said it would need to break even. Overnight figures show that the inaugural episode of the new-look season, which aired at 8 p.m.
Trump has been criticized in the past for giving far less of his income to charitable causes than many other multi-billionaires. President Donald Trump has already pledged $1 million in personal money to Harvey storm relief efforts.
For the first time, North Korea also specifically mentioned the possibility of a electromagnetic pulse, or EMP, attack. Kim signed off on the plan, but is watching the moves by the USA before deciding when or whether to carry it out.
The UNSC on Tuesday strongly condemned North Korea's firing of the ballistic missile, calling it an "outrageous" threat. Questions remain over whether Pyongyang has miniaturized its weapons and whether it has a working hydrogen bomb.
There would be regular exchanges and meetings between their foreign ministers and United Nations representatives, he said. BRICS consists of Brazil, Russia, India, China and South Africa.
Lukaku reveals major reason he chose Man Utd over Chelsea
Jose Mourinho has suggested that managers who leave a club "in conditions for failure" are more damaging than short-term bosses. He says United's quick business saved them almost £75m on Lukaku alone, explaining: "I think we were very clever".
Redskins Talked Su'a Cravens Out of Retiring
Cravens reportedly went through a similar situation as a rookie, no-showing for 1.5 days before the Redskins had to lure him back. Football has always been a risky sport, but recent research has provided insight into how life-threatening the game can be.
Eden Hazard Latest, Diego Costa Rumours
The 25-man squad lists had to be completed on Friday, with the Premier League confirming the selections on their official website. Costa has made it clear he wants to rejoin Atletico after being told he is not in Antonio Conte's Chelsea plans for the season.
Duchess of Cambridge expecting third child
On a royal tour of Poland in July 2017, Kate joked about having a third - after being given a present designed for newborns. However, Prince Harry will be pushed further down the line of succession by his newest nephew or niece.
Xiaomi Mi MIX 2 Has Entered Mass Production
We've collated all the specs, feature and release date rumours, so you're up to date on the imminent release from Xiaomi . Besides this, the screenshots also reveal the presence of 4400mAh battery in the Mi Mix 2 , along with a 20MP rear camera.