Pegula, who is now locked into the top-eight and therefore will qualify for the WTA Finals, struggled to win points on her serve in the opening set, but raised her 57 per cent success rate up to 69 per cent in the second set, and 66 per cent in the decider.
The American had to come from a break down in the second set to keep her tournament alive, and she will now face Canada's Bianca Andreescu in the third round.
Meanwhile, fellow United States star Coco Gauff was too good for Italy's Elisabetta Cocciaretto, winning 7-6 (7-1) 6-3 to book a third-round clash with another Italian, Martina Trevisan, who earned her way there with a 6-0 4-6 6-3 win over Katerina Siniakova.
The other two seeded Americans were also successful, with 13th seed Madison Keys coming from a set down to defeat Ajla Tomljanovic 3-6 6-4 6-3, and 14th seed Danielle Collins repelled the challenge of Magdalena Frech 6-3 6-4.
There were positive signs for former world number five Eugenie Bouchard, who ended up losing, but showed she still has her talent by taking a set off world number 23 Jelena Ostapenko in a 7-5 2-6 6-1 result.
Russian pair Anna Kalinskaya and Liudmila Samsonova both emerged in three-set outings, with Kalinskaya outlasting Elise Mertens 6-4 0-6 7-5, while Samsonova upset world number four Aryna Sabalenka 6-4 2-6 6-2.
World number 12 Veronika Kudermetova kept her WTA Finals hopes alive with a 6-4 7-5 win over Donna Vekic, and the Czech Republic's Marie Bouzkova ousted Colombia's Camila Osorio 6-3 6-1.
In the late window, Sloane Stephens eliminated Olympic gold medalist Belinda Bencic 6-4 6-4, and top overall seed Paula Badosa retired due to injury after losing the first set 6-2 against Victoria Azarenka.
American Keys, seeded fourth, surged clear of China’s Wang Xinyu in a dominant second set to prevail 7-5 6-0, only being broken once in the match.
Haddad Maia, meanwhile, fought back from losing the first three games to defeat Emma Navarro 6-4 7-6 (7-1) in a keenly contested battle.
Second seed Haddad Maia will face Liudmila Samsonova in the last eight, while Keys will take on either Ekaterina Alexandrova or Magda Linette at the WTA 500 event.
Top seed Marketa Vondrousova and two-time tournament winner Elina Svitolina are among the other players due to play later on Wednesday.
Data Debrief: Haddad Maia shows resilience
The battling win for Haddad Maia lasted two hours and 16 minutes, with Navarro pushing the Brazilian all the way.
Navarro forced 17 break points on Haddad Maia’s serve across the two sets and converted six of them, but still fell to defeat.
Haddad Maia now leads the head-to-head against Navarro 2-1, having also beaten her at the Madrid Open last month as part of her run to the last eight in Spain.
Halep landed 75 per cent of her first-serves and won those points at a rate of 82 per cent (27/33).
Martic's serve commanded much less respect, as she landed 69 per cent of her first-serves, but only won 36 per cent of those points (8/22).
After holding in her first service game, Martic allowed Halep to rattle off six consecutive games, with three double-faults assisting her Romanian opponent.
With the win, Halep booked a semi-final matchup against Poland's number three seed Iga Swiatek after she prevailed in her meeting with American Madison Keys in similar fashion.
The top seed donned the yellow and blue colours of her homeland for Tuesday's match and eased to a 6-2 6-1 victory in a little over an hour in Mexico.
Svitolina only agreed to play her opener after tennis authorities announced a ban on Russian and Belarussian players competing under the name and flags of their countries.
And as Russia's invasion of Ukraine entered its sixth day, the 27-year-old produced an impressive performance that saw her win 73.5 per cent of her first-serve points.
Former world number three Svitolina, who will now face Bulgarian qualifier Viktoriya Tomova, had previously announced she will donate her prize money to the Ukrainian army.
"It's a special one because of what we are going through right now in Ukraine, it's terrifying," Svitolina told reporters.
"It's been six days and all the Ukrainian tennis players and Ukrainians who are there, we have been really terrified with what is happening.
"For me, playing the match here, I'm not playing only for myself. I'm playing for my country, I'm playing for the help of the Ukrainian army and people in need.
"I was focused. I was on a mission for my country. From the beginning, it was important to be ready for anything that comes my way."
Petra Martic is also through to round two after recovering from behind to beat third seed Madison Keys 4-6 7-6 (7-3) 6-3.
Marie Bouzkova awaits following the world number 81's 4-6 6-2 6-4 win against Sara Errani. Number eight seed Ann Li's participation in the tournament came to an end with a 6-2 6-1 loss to Wang Xinyu, who will now face Brazil's Beatriz Haddad Maia.
World number 10 Jabeur had lost her previous four meetings with Kvitova, but she emerged victorious on Wednesday with a 6-4 6-4 win to reach the quarter-finals.
Jabeur recovered from 3-1 down in both sets at Ken Rosewall Arena and converted half of her six break points on her way to setting up a meeting with Kontaveit.
The two will resume their friendly rivalry after Kontaveit overcame Romanian qualifier Elena-Gabriela Ruse 6-3 6-1.
Jabeur lost out to Kontaveit for the last WTA Finals spot in November and is now seeking revenge in the final warm-up event ahead of the Australian Open.
"Anett is a great player. We had our moments last year," Jabeur said. "I told her, 'You're obsessed with me, you always follow me, so stop [smiling]'.
"I know the pressure is on me, not really on her. But maybe I can get some payback for last year."
Garbine Muguruza is also through to the last eight in Sydney thanks to a 6-1 7-6 (7-4) win against Ekaterina Alexandrova.
The two-time major champion will face Daria Kasatkina, who beat Elise Mertens 6-3 6-4, for a place in the semi-finals.
Third seed Barbora Krejcikova survived a brief fightback from Jaqueline Cristian to advance 6-1 7-5, meanwhile, and Paula Badosa beat home hope Ajla Tomljanovic 6-3 6-4.
There was disappointment for in-form Elena Rybakina, who thrashed Emma Raducanu on Tuesday but had to withdraw from her clash with Caroline Garcia with a thigh injury.
At the Adelaide International 2, Coco Gauff prevailed 6-3 5-7 6-3 in her battle of the teenagers showdown with Marta Kostyuk.
Gauff is one of five Americans in the quarter-finals along with Madison Brengle, Alison Riske, Lauren Davis and Madison Keys, who beat Tereza Martincova 6-1 6-3 to advance.
The world number 26, who was defeated by Amanda Anisimova in the Melbourne Summer Set 2 semi-finals last week, beat second seed Muguruza 6-4 6-4.
Kasatkina held throughout the opening set, landing 67 per cent of her first serves, and saw the job through in the second despite a couple of early breaks for Muguruza.
It is the Russian's first win over a top-five opponent since beating Caroline Wozniacki at the 2018 French Open.
She will now face fifth seed Paula Badosa, who saw off Olympic gold medallist Belinda Bencic 7-6 (8-6) 3-6 6-3 in an entertaining match lasting two hours and 35 minutes.
The other semi-final in Sydney will be contested between Anett Kontaveit and Barbora Krejcikova, who advanced past Ons Jabeur and Caroline Garcia respectively.
Krejcikova proved far too strong for Garcia, prevailing 6-0 6-2 in 70 minutes, while Kontaveit was in action for just 43 minutes before being handed a walkover win in her match.
Jabeur had targeted "payback" against Kontaveit after her quarter-final opponent pipped her to the final WTA Finals spot in November, but injury cost her the chance to do so.
Having lost the first set 6-4, Jabeur – who eliminated Petra Kvitova in the previous round – felt unable to continue due to a lower back injury.
At the Adelaide International 2, three of the five Americans in action made it through to the semi-finals.
Alison Riske's clash with compatriot Madison Brengle ended early due to the latter retiring with the first set level at 3-3. Tamara Zidansek awaits Riske after beating Lauren Davis 7-6 (7-4) 7-6 (9-7).
Coco Gauff and Madison Keys will meet in the other semi-final, meanwhile, following victories over Ana Konjuh and Ludmilla Samsonova in two and three sets respectively.
Number 15 seed Kerber was handed a banana skin tie of sorts against Zheng Qinwen and was made to work hard for her 6-2 5-7 6-4 victory against the rising Chinese star.
Zheng battled back with three breaks of serve in the second set to level up and led 4-1 in the decider, but her opponent dug deep to prevail in a time of two hours and 18 minutes.
Daria Kasatkina awaits Kerber – who had not previously won this calendar year – after the Russian beat Katie Volynets 6-4 4-6 7-5 earlier in the day.
Keys was also pushed all the way in her clash with Misaki Doi before coming out on top 6-4 3-6 6-1 to set up a meeting with Alison Riske in round three.
The Australian Open semi-finalist struggled in the second set after holding her serve throughout the first, though she had enough quality to see off her Japanese opponent.
Gauff had less trouble against fellow American Liu, advancing in a little over an hour to reach the third round, the stage in which she was eliminated on her debut here last year.
She will take on former world number one Simona Halep on Sunday, the day she turns 18, in a rematch of their last-16 showdown from Wimbledon three years ago.
Emma Raducanu and Iga Swiatek are among the others already through to the last 32 in California.
Madison Keys secured her place in the semi-finals of the Australian Open for the third time with a comeback win over Elina Svitolina.
Madison Keys is just two wins away from a maiden major title, but she does not need a grand slam trophy to be satisfied with her career.
The 29-year-old trailed 5-2 in the first set and 4-2 in the third set but rallied in both to come from behind to beat the number three seed.
Despite winning the second set, Gauff struggled to find her rhythm, suffering from 13 double faults, including two in the final game.
Keys will face former Madrid Open champion Ons Jabeur for a spot in the semi-final after the number eight seed overcame Jelena Ostapenko in straight sets.
Data debrief: Keys reaches new milestone
Having lost in the first round in seven of her nine previous trips to the Spanish capital, Keys has now bettered her previous best finish in Madrid - a third-round showing in 2016.
Keys hadn't won three matches in a row since reaching the US Open semifinals last year.
The 29-year-old trailed 5-2 in the first set and 4-2 in the third set but rallied in both to come from behind to beat the number three seed.
Despite winning the second set, Gauff struggled to find her rhythm, suffering from 13 double faults, including two in the final game.
Keys will face former Madrid Open champion Ons Jabeur for a spot in the semi-final after the number eight seed overcame Jelena Ostapenko in straight sets.
Data debrief: Keys reaches new milestone
Having lost in the first round in seven of her nine previous trips to the Spanish capital, Keys has now bettered her previous best finish in Madrid - a third-round showing in 2016.
Keys hadn't won three matches in a row since reaching the US Open semifinals last year.
The American third seed was beaten by China's Zhang Shuai 7-5 7-6 (7-5) in one hour and 39 minutes.
Keys sent down 7-1 aces but Zhang, ranked 51st in the world, was excellent on return, converting four of her 11 break points.
Fourth seed Daria Kasatkina was also in danger after losing the first set but rallied to win 3-6 7-5 6-3 over France's Caroline Garcia.
"It was a tough match. From my point of view, I think the level of the game was very good, and I'm really happy that I was able to turn the match in the second set," Kasatkina said in the on-court interview.
Ninth seed Alison Riske was emphatically beaten by Croatian Ana Konjuh 6-1 6-4 in one hour and 13 minutes, while sixth seed Petra Martic bowed out to Poland's Magda Linette 7-5 7-6 (7-5).
A 6-1 6-2 victory for Keys at Adelaide International 2 gave her a sixth WTA Tour title and a first since a stunning run in 2019 at Cincinnati.
Keys, who faces a tough Australian Open first-round clash against 2020 champion Sofia Kenin, showed her form is coming back after a lean spell.
The former world number seven has slipped to a lowly 87th in the rankings, but at the age of 26 she has ample time to climb back towards the top of the game.
This win moves her back into the top 60, with Elina Svitolina and Coco Gauff among the players Keys has fended off this week.
Keys said: "I'm really happy with how today went. There were a couple of opportunities where momentum could have switched, and I think I did a really good job of just regrouping and continuing to focus on my side of the court. Really happy to get a win."
Keys explained her mindset had been "dark" at times in 2021, with her appetite for tennis ebbing away.
She said: "Just knowing from what I was thinking about last year and the deep, dark pit of despair that I put myself into because of that, I don't want to go back to that. I don't want to let myself borderline hate being on the tennis court and hate competing. If I let myself think that way, that's where it goes."
Her motivation is on an upwards curve now, and results like this will help. Keys held serve throughout, did not face a break point, and broke Riske's delivery four times on the way to sealing victory in an hour and six minutes.
Quoted on the WTA website, Keys added: "I think the biggest takeaway is that things can switch at any moment. As long as you can continue to have the right mindset and keep going for things and keep working hard, things will get better if they're not going well, as long as you just have the right mindset and continue to have a good attitude about it."
Madison Keys won her first grand slam title at the 46th attempt on Saturday, upsetting Aryna Sabalenka to take the Australian Open crown.
The 2017 US Open runner-up announced on Thursday that she contracted COVID-19 before she was due to fly out for the first grand slam of the year.
Keys did not state she will definitely miss the major, which starts on February 8, but it appears the American will not make the trip to Melbourne.
The American wrote on Instagram: "Hi everyone, I wanted to let you know that I unfortunately tested positive for COVID-19 before I was supposed to fly to Australia.
"I'm very disappointed to not be able to play in the coming weeks after training hard in the off-season and knowing Tennis Australia and the tours did so much to make these events happen.
"I am self-isolating at home and will continue to follow all the necessary health precautions. I look forward to being back on tour next month."
It was revealed earlier in the day that three-time major winner Andy Murray has also tested positive for the virus, but still hopes to play in the Australian Open.
Meanwhile, world number 50 Tennys Sandgren was cleared to board a flight from the United States bound for Melbourne despite revealing he returned a new positive coronavirus test this week.
The American, twice a quarter-finalist at Melbourne Park, initially posted to social media on Wednesday that he had tested positive for the virus for a second time.
Although his first instance of having the illness was recorded in November, the 29-year-old's participation in the tournament appeared to be in doubt.
But as he continued to update followers through the day, it emerged he had been allowed to board his flight.
Players will only be allowed into Australia with proof of a negative test just prior to departure, or with approval to travel as a recovered case at the complete discretion of an Australian government authority.
Anyone wanting to travel out for the tournament who previously tested positive is required to provide additional and highly detailed medical information as proof they are a recovered case and no longer infectious or a risk to the community.
Keys arrived in the contest seeking a first career victory over a reigning world number one in six attempts, having failed to win a set in each of the previous five.
The 2019 champion had also lost her previous two showdowns with Swiatek, including a resounding 6-1 6-0 defeat in the Indian Wells Open quarter-finals earlier this year.
After the first games went with serve, Keys went into overdrive; reeling off nine successive games to take full command of the contest at 6-3 5-0.
Swiatek rallied as she rescued match point to avoid the bagel, winning 11 of 12 points to reduce the second-set deficit to 5-3.
The winner of six WTA titles this season, the Pole saved a further match point in the ninth game before claiming what appeared to be another crucial break of serve.
However, former US Open finalist Keys responded magnificently to make it third time lucky against Swiatek, who is now 4-4 since her 37-match winning streak ended with defeat by Alize Cornet at Wimbledon.
On her 46th main-draw appearance, Madison Keys is finally a grand slam champion following her stunning triumph at the Australian Open.
The world number four prevailed 0-6 6-4 7-6 (14-12) in a match that went the distance and will take on Paula Badosa, who beat in-form Daria Kasatkina in the other semi-final.
Krejcikova had lost five in a row against top-10 players and was soundly beaten in the first set, but she held in the second and earned the only break in the ninth game to level up.
That set up an incredible decider, which fourth seed Kontaveit led 6-5, but she could not take the first three of her match points as Krejcikova battled valiantly to force a tie-break.
Krejcikova felt her opponent's pain as she then squandered two match points of her own when leading 6-4.
It appeared neither player wanted to win as two more match points went begging for Krejcikova and four for Kontaveit in what turned into a real classic.
But Krejcikova eventually took her fifth opportunity to see off Kontaveit and reach a sixth WTA singles final.
"I think from both sides it was a really, really tough match," Krejcikova said. "I think we played wonderful tennis.
"It was very, very tight, and I'm really happy that I was able to hold the nerves better and that I won this match.
"I was just playing, just trying to fight for every single ball. When I had those match points down, I was just trying to figure out how to build up the point and how to win the point."
Badosa awaits Krejcikova in Saturday's final after beating Kasatkina in a match with far fewer twists and turns.
Competing in her second semi-final in as many weeks, it was similar disappointment for Kasatkina as she fell to a 6-2 6-2 loss.
French Open quarter-finalist Badosa hit 26 winners to Kasatkina's 12 and did not look back after winning 14 of the opening 16 points.
At the Adelaide International 2, meanwhile, it will be an all-American final as Madison Keys and Alison Riske advanced past Tamara Zidansek and Coco Gauff respectively.
Riske was given a walkover win against Zidansek, who withdrew with an abdominal injury, while Keys beat compatriot Gauff in three sets.
The 11th-seeded Kvitova defeated 2019 Western and Southern winner Madison Keys 7-5 6-4 on a rain-plagued opening day of main-draw play at the tournament outside Cincinnati, Ohio.
The Czech saved eight of nine break points against her serve while breaking Keys three times, and that was enough to pull out the victory.
Kvitova's countrywoman Barbora Krejcikova, the ninth seed, made her singles debut at the WTA 1000 event with a 6-3 6-2 rout of Daria Kasatkina.
Fifteenth seed Elise Mertens also was a straight-sets winner, taking down Nadia Podoroska 6-3 6-4, while 13th seed Jennifer Brady defeated Ekaterina Alexandrova 6-3 7-6 (7-3) in a match that finished shortly before 1 a.m. local time.
Though only Krejcikova was in action Monday, the field in Cincinnati includes nine of the top 10 players in the rankings, led by Ashleigh Barty and Naomi Osaka in their first appearances since the Tokyo Olympics.
In other matches on the first day of play, Heather Watson defeated Aliaksandra Sasnovich 6-2 3-6 6-1, while Paula Badosa outlasted Petra Martic 4-6 6-4 7-6 (11-9) in a two-hour, 34-minute marathon.
Yulia Putintseva breezed past Zhang Shuai 6-2 6-0, Jelena Ostapenko beat Tamara Zidansek 7-5 6-1 and Jil Teichmann downed Sorana Cirstea 6-2 6-0.
Angelique Kerber beat Maria Sakkari 6-2 6-2, with Alison Riske matching that scoreline in a defeat of Leylah Fernandez.
Shelby Rogers won 6-4 2-1 when her countrywoman Danielle Collins retired with an injury.
The two-time Wimbledon champion battled to a 6-7 (6-8) 6-4 6-3 victory in two hours and 18 minutes, saying the match had been "mentally so tough".
Both players had taken significant scalps to reach this stage, with Keys knocking out world number one Iga Swiatek and Kvitova ousting Wimbledon runner-up Ons Jabeur.
Kvitova reached semi-finals at Cincinnati in 2012 and 2018 and lost three-set battles on both occasions, but this time she came good in the decider to earn a first final appearance at the event and a 40th overall in her WTA career.
The 32-year-old Czech slipped an early break adrift in the opening set before fighting back to force a tie-break. She came from behind in that, too, to level up at 6-6, only for hard-hitting American Keys to win the next two points, the first with a sizzling backhand winner.
Kvitova sensed she was still firmly in the match, however, and surges to 3-1 in each of the next two sets provided the platform to fully turn around the contest.
A 12th WTA 1000-level final awaits her, and she will go to 20th in the rankings should she lose Sunday's final and up to 15th if she carries off the title.
Kvitova said of her win: "It was incredibly tough. I expected it would be tough, but I didn't expect it that tough. Madison played unbelievable.
"She played an amazing tie-break, but I tried to keep going, be there and be a little calmer than before and wait for the chances. It was an incredible match, and I'm really happy that I made it somehow.
"I don't really care about the ranking. Being in the final, that's more important, and that's why I'm playing tennis: to be in finals and fighting for a trophy."
She awaited the winner of the second semi-final between Aryna Sabalenka and Caroline Garcia.
