Kenin blitzed Anastasija Sevastova 6-2 6-2 to get the USA up and running in Everett, while Williams battled past 2017 French Open winner Jelena Ostapenko 7-6 (7-4) 7-6 (7-3).
Barely a week after breaking through for her first grand slam title in Melbourne, Kenin was in the American state of Washington to represent her country.
The world number seven and 21-year-old surged past Sevastova before 23-time major winner Williams eventually saw off Ostapenko in the second rubber to improve her win-loss record at the Fed Cup to 14-0.
"It's been a long journey. It wasn't easy," Kenin said. "But I was super happy to come here and play with the team."
It was a tough day for former world number one and two-time grand slam champion Naomi Osaka, who was reduced to tears after losing to unheralded Spaniard Sara Sorribes Tormo.
Osaka, whose title defence at Melbourne Park was sensationally ended by teenager Coco Gauff in the third round, was swept aside 6-0 6-3 against Sorribes Tormo.
Japan trail Spain 2-0 in the tie after Carla Suarez Navarro accounted for Misaki Doi 6-3 6-4.
Switzerland, led by Belinda Bencic, Germany and Slovakia also boast 2-0 leads against Canada, Brazil and Great Britain respectively.
The other ties – Netherlands against Belarus, Romania versus Russia and Belgium against Kazakhstan – are deadlocked at 1-1.
Belarus proved no match for Australia, who got the job done across their two singles matches on the day in the Czech Republic.
Storm Sanders got the ball rolling as she comfortably saw off Yuliya Hatouka 6-3 6-3 in the first contest of the day in Group B.
Ajla Tomljanovic was made to work a little harder by Aliaksandra Sasnovich as she lost the first set but eventually rallied to overcome her opponent 4-6 6-2 6-3.
It meant the two countries' doubles meeting was a dead rubber – Belarus at least took the opportunity to avoid a 3-0 annihilation as Sasnovich teamed up with Lidziya Marozava in the 6-4 6-4 defeat of Olivia Gadecki and Ellen Perez.
In Group D, Switzerland and the Czech Republic claimed one victory apiece in the singles – Marketa Vondrousova had too much for Viktorija Golubic in a 6-4 6-2 success that gave the Czechs the upper hand.
But Belinda Bencic levelled things up despite the unenviable task of facing world number three Barbora Krejcikova, emerging with a 7-6 (7-2) 6-4 success.
Bencic was then involved in the doubles decider as well, getting the better of Lucie Hradecka and Katerina Siniakova with Jil Belen Teichmann, their 6-3 6-3 win sealing the semis spot for the Swiss.
The Russian Tennis Federation – who eliminated defending champions France on Wednesday – and the United States are due to contest the other semi-final.
Germany lost to hosts Czech Republic on the opening day and were brushed aside 3-0 by Switzerland on Tuesday, with world number nine Kerber losing 5-7 6-2 6-2 to Bencic.
Kerber was carrying an injury and was outlasted by the Olympic gold medallist, with that triumph coming after Viktorija Golubic defeated Andrea Petkovic 6-4 7-5.
Golubic and Jil Teichmann added further gloss to the scoreline by overcoming Anna-Lena Friedsam and Nastasja Mariana Schunk in the doubles.
Switzerland will now meet the Czech Republic in a winners-takes-all contest to determine who finishes top of Group D.
The upset of the day came in Group B as Australia beat Belgium 2-1, with Daria Gavrilova kicking things off by beating Greet Minnen 6-4 1-6 6-4.
Storm Sanders then battled back to beat Elise Mertens 4-6 7-6 (7-5) 6-0, rendering Mertens and Minnen's doubles win nothing more than a consolation.
In Group A, Russia cruised to a 3-0 win over Canada.
Daria Kasatkina beat Carol Zhao 6-3 6-1 and Anastasia Pavlyuchenkova was too strong for Rebecca Marino as she prevailed in three sets.
Slovakia top Group C, meanwhile, after beating the United States 2-1. Shelby Rogers fell 6-4 6-4 to Viktoria Kuzmova before Danielle Collins levelled with a 6-3 6-2 win against Anna Karolina Schmiedlova.
That set up a decider in the doubles, which went the distance as the Slovakian pair of Kuzmova and Tereza Mihalikova prevailed 6-2 6-7 (5-7) 12-10 in a thriller with Caroline Dolehide and CoCo Vandeweghe.
Andreescu has not played since injuring her knee in her match against Karolina Pliskova at the WTA Finals at the end of October.
She pulled out of the Auckland Classic and then the Australian Open as her start to 2020 was delayed by her recovery, having also struggled with a host of other injury issues last year.
Andreescu is in Biel with her Canada team-mates for the Switzerland tie, which will be played over February 7 and 8.
World number five Belinda Bencic, who Andreescu beat in the semi-finals at Flushing Meadows, is one of her possible opponents this week.
"She has been training and she is improving every day – we are taking it day by day," said Canada captain Heidi El Tabakh.
"We know that, for this tie, time is against her, but she's been making a lot of improvements.
"She still has a couple of days left. As of right now, we haven't made any decisions yet about the team, but we will when the time comes."
Andreescu told Tennis Canada: "I think there's still a chance. We haven't made any decisions yet but I'm hoping I can play."
Switzerland are preparing as if Andreescu will play in the tie, which is one of eight contests which will decide the teams to join Australia, France, Czech Republic and Hungary for the inaugural Fed Cup Finals in Budapest in April.
"I have to assume Bianca Andreescu is going to walk out there and compete because why else would she be here?" said Switzerland captain Heinz Guenthardt.
"Nobody knows how well she'll compete - probably even she doesn't know that.
"It's a different thing to practice and then walk out there and play a Fed Cup tie.
"It doesn't sound like a very thought out answer, but in the case of this week particularly we're just going to try to focus on ourselves.
"We have a good group. Belinda is obviously our number one and then we have four players who can on their given day represent Switzerland."
The qualifying round contains some impressive line-ups, with Serena Williams, Australian Open champion Sofia Kenin and teen star Coco Gauff among the United States team playing Latvia, while Naomi Osaka leads Japan against Spain.
The tournament, formerly known as the Fed Cup, kicked off in exciting fashion with three of the four ties going to a final rubber match.
The most notable result of the day came in Group A as the lowest-ranked team Canada beat the reigning champions France 2-1. A singles win for world number 353 Francoise Abanda against Fiona Ferro was followed by the pairing of Gabriela Dabrowski and Rebecca Marino defeating Clara Burel and Alize Cornet to clinch it.
Elsewhere, Group D began with hosts Czech Republic beating Germany 2-1, despite world number three Barbora Krejcikova losing to world number nine Angelique Kerber in the second match.
The Czechs have won six of the last nine Fed Cups, and will be hoping to reclaim the crown in their home tournament.
History was made by Belgium's Greet Minnen in Group B as she became the first person to win a match in the competition’s new format, beating Iryna Shymanovich of Belarus 6-2 6-2. Elise Mertens sealed the win for the Belgians immediately after, though Belarus won the dead rubber doubles contest.
In Group C, Spain were able to overcome Slovakia in their deciding doubles match as Sara Sorribes Tormo and Carla Suarez Navarro beat Viktoria Kuzmova and Tereza Mihalikova.
Day two sees Canada take on the Russian Tennis Federation, while Australia start their tournament against Belgium, Slovakia face USA, and Germany will look to get back on track against Switzerland.
Due to be hosted in Madrid, the Davis Cup Finals were supposed to have taken place from November 23-29, but following a three-month review it was deemed too challenging to stage this year.
Organisers Kosmos Tennis and the International Tennis Federation (ITF) pointed to the fact more than 90 athletes would have been expected to be involved, while the international event attracts thousands of fans, officials, staff and other stakeholders from across the globe, with many countries at differing stages of the pandemic.
With the competition now set to begin on November 22, 2021, it was confirmed the 18 teams that have already qualified for the men's global team tournament will have their places secured, while the draw for the finals remains the same.
Kosmos president and Barcelona defender Gerard Pique said: "It's a huge disappointment for all of us that the Davis Cup Finals will not be held in 2020.
"We don't know how the situation will develop in each qualified nation, or if restrictions in Spain will remain sufficiently eased, as such it is impossible to predict the situation in November and guarantee the safety of those travelling to Madrid.
"This postponement has no long-term bearing on our collective ambitions for the Davis Cup. The ITF and Kosmos Tennis look forward to delivering an outstanding competition in 2021, when it is safe and feasible to do so."
The women's equivalent, the Fed Cup, has also unsurprisingly hit a similar stumbling block and will now take place from April 13-18.
Budapest remains its location and, much like the Davis Cup, the teams that have already qualified will retain their places. The Fed Cup Play-offs will go ahead at the start of February.
Neither postponement has come as a surprise, particularly following the chaos caused by the Adria Tour event earlier this month.
Organised by world number one Novak Djokovic and played across locations in Serbia and Croatia, the event did not adhere to social distancing procedures and attracted large crowds. Legs in Montenegro and Bosnia-Herzegovina were ultimately postponed due to COVID-19 concerns.
Several of the marquee players ended up testing positive for the virus, including Djokovic himself, Grigor Dimitrov, Borna Coric and Viktor Troicki, and the event was met with widespread criticism.
Multiple sporting events have been either suspended or cancelled in recent weeks as the virus continues to spread around the globe.
In Italy, all sporting events until April 3 have been postponed, while football matches across Europe are to continue to be held behind closed doors.
Earlier this week, the Indian Wells tournament – due to take place in California – was cancelled due to fears over the virus, which on Wednesday was declared as a global pandemic by the World Health Organisation.
The ITF has now taken the decision to postpone the Fed Cup finals, which were due to be held in Hungary between April 14 and 19 at the Laszlo Papp Sport Arena in Budapest, while the play-offs – set to take place on April 17 and 18 in eight different locations – have also been put on hold.
"After careful consideration and close discussion with the ITF Board, the Local Organising Committee and in light of [Wednesday's announcement by the Hungarian government regarding indoor events, it is with regret that the ITF has announced the postponement of the Fed Cup Finals," a statement on the Fed Cup's official website read.
"The ITF is committed to delivering the Fed Cup Finals in 2020 and is in consultation with key stakeholders, including the Hungarian Government, the Hungarian Tennis Association (HTA) and the Women’s Tennis Association (WTA) to find a suitable alternative date for the tournament."
The Fed Cup is an Olympic Qualification event and the ITF has pledged to work alongside the International Olympic Committee (IOC) to address any impact the postponement may have on athletes' eligibility for Tokyo 2020.
"We are extremely disappointed to have to make this decision, but we will not risk the safety and welfare of players, captains, event staff or spectators," said ITF president David Haggerty.
"This decision has not been made lightly; the threat posed by the COVID-19 is a serious one and calls for us to act responsibly as a federation and as human beings. This situation goes beyond sport."
Clara Burel put France on course for the 3-0 victory they needed to advance from Group A with a three-set victory over Ekaterina Alexandrova, but Anastasia Pavlyuchenkova outlasted Alize Cornet in the second rubber to ensure a new champion will be crowned.
Pavlyuchenkova saved six of 10 break points and racked up an impressive 34 winners en route to a crucial 5-7 6-4 6-2 success against Cornet.
"I'm so, so happy and so proud of myself because I think it was an incredible match. It was very good tennis but more importantly I think it was an amazing fighting spirit from both of us," said Pavlyuchenkova.
"We were like two tigers. Nobody wanted to give the other anything and I think that's what matters. That's the sport we're playing."
Veronika Kudermetova and Liudmila Samsonova comfortably defeated Cornet and Burel in the doubles to consign the reigning champions to a 2-1 defeat.
The RTF will go up against the USA in the first semi-final, with the Americans comfortably seeing off Spain in the singles rubbers.
Sloane Stephens bested Nuria Parrizas-Diaz 6-4 6-4 before Danielle Collins swept Sara Sorribes Tormo aside 6-1 6-0 in under an hour.
Collins won 83 per cent of points behind her first serve and forced Sorribes Tormo into 24 errors during a resounding victory.
Spain avoided a 3-0 defeat, though, with Aliona Bolsova and Rebeka Masarova beating Caroline Dolehide and CoCo Vandeweghe 6-3 6-4 in the doubles rubber.
Fifteen-year-old Gauff and Williams, 38, were named in a formidable-looking five-player squad for the qualifying tie against Latvia, which will be played in the city of Everett, near Seattle.
Gauff is in line to become the second-youngest player to represent the US in the Fed Cup, if she sees action in the two-day tie.
Only Jennifer Capriati has played at a younger age, with the future grand slam winner and world number one being just 14 years and four months old in 1990 when she played against Poland.
Joining Gauff and Williams will be Sofia Kenin, who has reached the semi-finals of the ongoing Australian Open, plus world number 19 Alison Riske and doubles specialist Bethanie Mattek-Sands.
World number nine Williams saw her hopes of landing a record-equalling 24th grand slam singles title in Melbourne dashed by a shock third-round defeat to China's Wang Qiang.
It was a result that prompted Williams to indicate she would work harder than ever to push for the record.
The veteran has never lost a Fed Cup singles match, being the holder of a 13-0 record, putting her two wins short of matching Martina Navratilova's career 15-0 mark.
Gauff went one round further than Williams in Australia before losing to compatriot Kenin, with the teenager having claimed the scalps of Venus Williams and defending champion Naomi Osaka on her run.
The US Fed Cup team is captained by former top-10 player Kathy Rinaldi, with the Latvia tie to be played on February 7-8.
Latvia have world number 33 Anastasija Sevastova and former French Open champion Jelena Ostapenko in their ranks.
A new Fed Cup format sees the winners of the eight February ties go on to compete at the 12-team Finals, which takes place in Budapest from April 14-19, with Australia, France, Hungary and Czech Republic already assured of their places.
Former world number one Halep was due to face Australia's Daria Saville in the round of 64 on Thursday but felt unable to contest the match.
Halep said she sustained a thigh injury during her Indian Wells semi-final defeat to Iga Swiatek the previous week and it caused her discomfort again while training on Wednesday.
The 30-year-old two-time major winner expects to sit out the Charleston Open and will miss the start of the Billie Jean King Cup.
In a tweet posted on her official Twitter account, Halep wrote: "While I was practising in Miami yesterday I felt a sharp pain in my left leg.
"I had been struggling with the thigh since my semi-final in Indian Wells and hoped it would improve, but I went for an MRI last night and unfortunately it showed a tear.
"My body needs time to heal and as a result I will be out of competition for three weeks. This means I have had to make the super tough decision to pull out of Miami, Charleston and Fed Cup [Billie Jean King Cup].
"While it feels like really disappointing news to share, I am keeping the confidence from my great start to the year and am motivated to do everything to be ready for the clay-court season.
"Thanks for your continued support through the highs and lows."
Lucky loser Harmony Tan will take Halep's place in the draw.
The former US Open champion had been named as part of Great Britain's team for the tournament, which will take place at Emirates Arena in Glasgow between November 8-13.
Raducanu was selected alongside Harriet Dart, Katie Boulter and Heather Watson, with a fifth member to be added at a later date, and made her Billie Jean King Cup debut in April's qualifier against Czech Republic.
However, after pulling out of the Transylvania Open earlier this month with the same right-wrist issue, the 19-year-old confirmed on Friday she had been told by doctors she will not recover in time.
"It's disappointing to get the news from the doctors that I won't be ready in time, particularly with it being on home soil," Raducanu said.
"I tried to do everything possible to get it ready in time.
"Since my last tournament I've been working every day on physical training and rehab. I've got confidence in my team-mates and look forward to playing next year."
Great Britain will be one of 12 teams participating in Scotland, and have been drawn in a group with Kazakhstan and Spain.
Russia, who won both competitions in 2021, have been suspended from competing in international team events following the country's invasion of Ukraine.
As the highest-ranked losing semi-finalist from last year, Serbia will take Russia's place in the Davis Cup Finals.
The wild card previously handed to Serbia will now go to one of the 12 nations knocked out in the qualifiers that took place earlier this month.
Likewise, as the highest-ranked side among the 2021 losing Billie Jean King Cup semi-finalists, Australia will replace Russia in that competition.
Australia were due to take part in April's qualifiers, but opponents Slovakia will now receive a bye and advance directly to the Finals.
Belarus have also been barred from competing in both events, meaning Belgium will receive a walkover in their qualifying match and advance to the Billie Jean King Cup Finals.
The Russians will meet Switzerland in the trophy showdown on Saturday, after Olympic champion Belinda Bencic defeated Ajla Tomljanovic to secure an unassailable 2-0 lead for the Swiss over Australia.
While Switzerland did not need a doubles decider, the Russian team, who are competing this week as Russian Tennis Federation, did.
Samsonova, who clinched her maiden singles title on the WTA Tour earlier this year, put them ahead in their tie against the USA, downing 2017 US Open champion Sloane Stephens 1-6 6-4 6-3.
Yet the USA hit back through Danielle Collins, who defeated Anastasia Pavlyuchenkova 6-7 (9-11) 7-6 (7-2) 6-2 – a contest that lasted two hours and 42 minutes in Prague.
Momentum was with the 18-time champions, but the Russians recovered in the doubles, with Samsonova and Kudermetova ultimately having little trouble in seeing off Shelby Rogers and Coco Vandeweghe 6-3 6-3.
Bencic saw off Tomljanovic to confirm Switzerland's place in the final, with Jil Teichmann having earlier overcome Storm Sanders 6-0 6-3.
Russia dominated this event, previously known as the Fed Cup, in the mid to late 2000s, winning four out of five editions from 2004 to 2008, but they have not triumphed since. Switzerland recorded their best result when a team featuring Martina Hingis finished second to Spain, way back in 1998.
After Daria Kasatkina swept to a 6-2 6-4 win over Jil Teichmann to put the Russians ahead against Switzerland, Samsonova produced a high-quality performance to win 3-6 6-3 6-4 against Bencic.
It meant there was no need for a doubles decider, with the Russian squad taking the match 2-0.
Samsonova had not expected to be involved in the singles contest in Prague, but a knee problem forced Anastasia Pavlyuchenkova to pull out just minutes before Saturday's final got under way, forcing Russian captain Igor Andreev into a reshuffle.
A worthy substitute, Samsonova is ranked 40th in the world, while Bencic sits at number 17, and this win was the Russian's third victory in three meetings this year with the Tokyo 2020 gold medallist.
One of those came in the final of the Berlin grass-court tournament, and the 22-year-old was not over-awed by another big occasion this time.
Just as she did in Berlin, Samsonova lost the opening set but then dominated, and by doing so she secured a fifth Russian triumph in this team competition, previously known as the Fed Cup.
Samsonova said: "I have too many emotions now. It's unbelievable. I'm unbelievably happy. It was an incredible fight. It was a more nervous game. It was more than tennis."
Andreev spoke of the strong bond in his squad, saying: "It's an historical win for us. It's been a long time without any trophies in team tennis. I'm very proud and very happy for the girls, the way they played.
"They're amazing, they're heroes, and they achieved this because they're a team – a real team – and real friends."
Russia dominated this event from 2004 to 2008, winning four of five titles, while Switzerland had only previously been to one final, when Martina Hingis and Patty Schynder were outmatched by Arantxa Sanchez Vicario and Conchita Martinez in the 1998 showpiece.
Trailing 2-0 in Washington, Latvia's fightback started with Jelena Ostapenko's win over Australian Open champion Sofia Kenin.
Williams' unbeaten record in singles was then ended by Anastasija Sevastova, who recorded a shock 7-6 (7-5) 3-6 7-6 (7-4) victory over the 23-time grand slam champion.
But USA moved into April's Fed Cup Finals thanks to Kenin and Bethanie Mattek-Sands, the duo winning the doubles over Ostapenko and Sevastova 6-4 6-0.
Belarus needed a thrilling doubles rubber to overcome the Netherlands 3-2.
Aryna Sabalenka and Aliaksandra Sasnovich edged Kiki Bertens and Demi Schuurs 4-6 6-3 7-6 (10-8).
Russia survived a test against Romania to prevail 3-2, Switzerland claimed a 3-1 success over Canada and Slovakia beat Great Britain 3-1.
Germany swept Brazil aside 4-0, Spain were too strong for Japan 3-1 and Elise Mertens led Belgium past Kazakhstan 3-1.
The world number 20 revealed she had been struggling with a back injury that affected her preparations for tournaments, falling at the first hurdle in each of her past two events.
Svitolina, the 2018 WTA Finals champion, reached the last eight at the Monterrey Open, where she refused to play Anastasia Potapova unless the Russian was classed as a neutral athlete at the start of the month, but she lost in her first match at both Indian Wells and the Miami Open.
Svitolina's sabbatical means she will be absent from Ukraine's Fed Cup clash with the United States next month, and it remains to be seen if she will return in time for the French Open at the end of May.
The 27-year-old posted on Twitter: "It's been an extremely difficult couple of months for me not only mentally, but physically.
"For quite a long time, I've been struggling with my back; the pain didn't let me prepare for the tournaments at my best.
"Meanwhile, observing with unbearable pain in my heart what is happening in my homeland of Ukraine and with how much bravery and courage our Ukrainian people are defending our country, this gave me a huge push to continue and fight on court.
"Now, my body can't handle it anymore and I need to rest, therefore I'm sad to announce that I will be missing the Fed Cup and a few of my favourite tournaments in Europe. But, I'm sure I will see you around soon, thank you for all your support in this challenging period."
Last month saw Osaka surrender her Australian Open crown when she lost to American teenager Coco Gauff in round three, and Friday's loss was a further blow in the early stages of 2020.
The 10th-ranked Japanese star lost 12 of the first 13 points on her serve on the La Manga clay and dropped the opening set in just 27 minutes.
She broke Sorribes Tormo's serve to establish a 2-0 lead in the second set but soon surrendered that advantage and was broken to love on her way to a sorry loss.
Spain captain Anabel Medina Garrigues said, according to the Fed Cup website: "We knew that Sara had the tools to make it very uncomfortable for Naomi. She stuck to the game plan perfectly."
Osaka let her emotions show by the final game and served a double fault on match point.
Spain went 2-0 ahead in the tie when Carla Suarez Navarro beat Misaki Doi 6-3 6-4 in the second rubber.
Suarez Navarro is set to face Osaka on Saturday's reverse singles, when Spain will need one more victory to book a place in the 12-team finals, to be played in Budapest in April.
