Back after more than seven years off the WTA Tour, Clijsters fell to a second straight loss, going down to second seed Johanna Konta 6-3 7-5 in the first round.
Clijsters, a wildcard at the WTA International tournament, managed to win just 12 return points in the 85-minute loss as Konta posted her first win of the year.
The four-time grand slam champion has been handed two tough draws this year, having lost to Garbine Muguruza in Dubai last month.
Playing for the first time since last year's US Open, seventh seed and last year's runner-up Azarenka was beaten 6-2 6-2 by Tamara Zidansek.
Top seed Elina Svitolina cruised through the opening round with a 6-3 6-2 victory over Danka Kovinic.
American 10th seed Lauren Davis also eased through, while there were wins for Anastasia Potapova, Leylah Fernandez, Arantxa Rus, Kateryna Bondarenko and Tatjana Maria.
Last year's US Open runner-up came through 6-1 4-6 7-6 (7-3) in two hours and 42 minutes to continue the defence of the title she won last March.
Fernandez won a marathon second game on her eighth break point and consolidated that break with a second to go 5-1 ahead in a one-sided first set.
She served out the opener at the third time of asking, but Zheng was beginning to find her feet in the contest and threatened the Fernandez serve early in the second set.
Zheng's first break points finally came at 5-4 and she took her chance to level the contest against the 19-year-old.
But Fernandez outlasted Zheng in a tense decider that went the distance after both players held serve, the second seed aggressively attacking her opponent to take the tie-break 7-3.
Fifth seed Camila Osorio ended the challenge of home hope Marcela Zacarias, meanwhile, the Colombian winning 7-6 (7-3) 6-3.
She will next face either top seed Elina Svitolina or Viktoriya Tomova in the last eight.
Brazil's Beatriz Haddad Maia was a 6-2 6-2 winner against Xinyu Wang and will contest a quarter-final against either Marie Bouzkova or Petra Martic.
Sara Sorribes Tormo was also a straight-sets winner in Wednesday's action, the fourth seed easing past Harmony Tan 6-2 6-2.
Canadian teenager Fernandez reached her second career WTA Tour singles final thanks to a 7-5 7-5 win over seventh seed Sara Sorribes Tormo.
The 18-year-old Fernandez – whose first final came via last year's Mexican Open in Acapulco, where she lost – converted six of nine break points and hit 35 winners.
Standing in Fernandez's way is Switzerland player Golubic.
Golubic upstaged eighth seed Ann Li 6-2 6-4 to become the first qualifier to advance to the Monterrey Open final in the tournament's history.
The 28-year-old Golubic also reached the Lyon Open final two weeks ago – beaten by Clara Tauson.
Fernandez broke through with a comfortable 6-1 6-4 victory over qualifier Viktorija Golubic on Sunday.
Featuring in her second WTA final after losing last year's Mexican Open in Acapulco, the 18-year-old Fernandez ensured she got her hands on the trophy this time.
Fernandez did not drop a set throughout the WTA International tournament, easing past her Swiss opponent in one-and-a-half hours.
Fernandez cruised into the last eight of the WTA International tournament on Wednesday by defeating Slovakia's Kucova 6-1 6-4 in Mexico.
Kucova had eliminated top seed and 2017 US Open champion Sloane Stephens on Tuesday, but she was no match for the 18-year-old Fernandez midweek.
Next up for Fernandez is Viktoria Kuzmova, who beat lucky loser Harriet Dart 6-4 6-3.
Spanish seventh seed Sara Sorribes Tormo did not have to take to the court, benefiting from a walkover after Kaja Juvan withdrew.
Sorribes Tormo will face Anna Karolina Schmiedlova, who outlasted Jasmine Paolini 2-6 6-2 6-2.
Monterrey Open defending champion Fernandez won 6-2 6-2 over the Slovakian, with the Canadian second seed dominant in all aspects as she triumphed in one hour and eight minutes.
In the longest match of the day, fourth seed Sara Sorribes Tormo needed more than three hours to edge Kamilla Rakhimova 7-5 6-7 (2-7) 6-1.
Fifth seed Camila Osorio defeated Magdalena Frech 6-3 7-6 (8-6), while Briton Heather Watson won 6-3 2-6 7-6 (7-4) over Jule Niemeier.
Harmony Tan, Marcela Zacarias, Viktoriya Tomova and Beatriz Haddad Maia were other winners on Monday.
Seeded ninth for the WTA International tournament, Japan's Hibino was upstaged 3-6 6-2 6-3 by Jasmine Paolini on Monday.
American eighth seed Li, however, had no such trouble in her 6-3 7-5 victory over Arantxa Rus on the outdoor hard courts.
Coco Vandeweghe – the 2017 Australian Open semi-finalist – suffered another early exit in Mexico.
After being ousted by Mihaela Buzarnescu in the opening round in Guadalajara last week, former world number nine Vandeweghe was eliminated 6-3 6-2 by Canadian teenager Leylah Fernandez.
Fernandez will face either top seed Sloane Stephens or lucky loser Kristina Kucova in the second round.
Anna Karolina Schmiedlova, Nina Stojanovic, Viktoria Kuzmova, Lauren Davis and Tamara Zidansek also progressed from the opening round.
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.
After a creditable performance in defeat to Australian Open runner-up Garbine Muguruza at the Dubai Tennis Championships last month, the 36-year-old's return to the sport continues this week.
She meets world number 16 Konta in the first round on Tuesday and continues to make positive steps.
"I feel like with the tennis that I've been playing, I'm improving," four-time grand slam winner Clijsters said ahead of her match in Mexico.
"In practice, I'm moving better, I'm reacting better, I'm making better decisions.
"It has to happen in the match now. The more matches I get to play, the more that will improve a little bit, and we'll see how far I can go.
"I still have a good level in me. I've played one official match so far and some practice sets so I would like to have more matches. That's the only way that I can practice certain things that you can only learn from matches."
The 6-2 7-6 (8-6) loss to Muguruza in Dubai was Clijsters' first contest since losing to Laura Robson in the second round of the US Open in August 2012.
Clijsters is braced for disappointments and setbacks in her return to the tour, but understands she will have to go through that in order to be competitive once more.
"It's a process of ups and downs," she said. "That is something you have to understand.
"It comes with failure, but I think it's how you deal with the moments where it's the toughest. That is when you improve the most, when you learn the most about yourself and when you are capable of improving.
"That was something I was always able to do well. When I lost in the past I was disappointed, but after a certain amount of time, I was able to make that switch in my head and use it, and that's how I was able to become better.
"It's that kind of mindset. It's important to not get discouraged about the losses and use it to motivate you even more."
Clijsters can take optimism from the fact Konta has lost all three of her matches in 2020, with the Briton having never played her before.
Ukraine's Kostyuk prevailed in a closely contested battle against the highest seed remaining in the field, taking the only break of the first set after saving four Collins break points the game prior.
The two women traded breaks to begin the second set, but the 20-year-old Kostyuk was too strong down the stretch, winning five of the final six games.
It will also be the first WTA-level final for her opponent, with unseeded 22-year-old Russian Varvara Gracheva overcoming American Katie Volynets 6-4 5-7 6-4.
The two-and-a-half-hour clash was tight all the way through, with Gracheva only narrowly edging the total point count 101-94.
Meanwhile, down south of the border at the Monterrey Open, world number five Caroline Garcia won her semi-final against Elise Mertens 6-3 6-4.
The reigning WTA Finals champion will have a chance to collect the 12th singles title of her career, and her first of the season, when she meets Croatia's Donna Vekic in the final.
Vekic, the third seed, emerged the 7-5 6-2 victor against China's Zhu Lin, continuing a red-hot run of form that has seen her win 13 of her past 15 matches dating back to New Year's Eve.
France's Garcia, the world number five and top overall seed, needed just 63 minutes to see off her Spanish challenger. She controlled the contest with her serve, taking the ace count eight to two while winning 75 per cent of her total service points (33-of-44).
She will now face Egypt's Mayar Sherif in the quarter-final after the seventh seed survived a tough 3-6 7-6 (8-6) 6-4 test from China's Wang Xinyu.
Fourth seed Elise Mertens emerged the 6-3 3-6 6-2 victor against Romania's Elena-Gabriela Ruse, while rising 22-year-old Italian Elisabetta Cocciaretto prevailed 7-6 (7-5) 7-6 (7-3) against Germany's Tatjana Maria.
North of the border in Austin's ATX Open, Danielle Collins ripped off a 67-minute 6-1 6-1 drubbing of Caty McNally to advance to the quarter-final.
Collins will meet Russia's Anna Kalinskaya next after the 24-year-old's convincing 6-3 6-1 victory over veteran CoCo Vandeweghe.
Eighth seed Marta Kostyuk is one of only three seeded competitors remaining after storming home in a 6-3 3-6 6-0 battle with Madison Brengle, and Germany's Anna-Lena Friedsam won the longest match of the day in a 7-5 6-7 (2-7) 7-6 (10-8) three-hour war of attrition against 18-year-old Russian Erika Andreeva.
Stephens – the American fifth seed – ended her drought by outlasting Emma Navarro 6-4 5-7 6-1 in Monterrey on Monday.
Prior to this week, Stephens had featured in four tournaments without a win, including a first-round exit at the Australian Open.
But the 2017 US Open champion finally opened her account for the year via the WTA International event after two hours, 17 minutes.
Former world number one Williams and her winless year continued, however, following a 4-6 6-3 6-2 defeat to qualifier Anna Karolina Schmiedlova.
Seven-time grand slam winner Williams battled but the 39-year-old was eventually eliminated after two hours, 29 minutes on court.
Elsewhere, Wang Yafan, Rebecca Peterson, Olga Govortsova, Astra Sharma and Marie Bouzkova progressed to the second round.
Stephens broke through for her first win of 2020 to book her spot in Wednesday's second-round match following a difficult start to the year.
But the American fifth seed was upstaged by 17-year-old Fernandez, who rallied past the 2017 US Open champion in three sets midweek.
Fernandez was a surprise finalist at last week's Mexican Open in Acapulco, where the Canadian reached her maiden WTA decider.
The in-form teenager moved through to back-to-back quarter-finals after prevailing in more than two hours against Stephens, with either top seed Elina Svitolina or Olga Govortsova awaiting.
Elsewhere at the WTA International event, sixth seed Rebecca Peterson defeated Kateryna Bondarenko 7-6 (7-2) 7-5, seventh seed Wang Yafan outlasted Astra Sharma 7-6 (7-5) 4-6 6-3 and ninth seed Marie Bouzkova beat Anna Karolina Schmiedlova 6-4 6-1.
Stephens went into the Mexico event as top seed but lost to Slovakian world number 151 Kristina Kucova 6-2 6-2.
The 27-year-old American is now 0-4 to start the 2021 WTA Tour season and has won only one set all season.
Stephens, now ranked 48th in the world, only managed to win 32.4 per cent of points on her first serve, with Kucova converting seven of 14 break points in the match.
Second seed Nadia Podoroska was also a first-round casualty on Tuesday, going down 6-4 6-4 to Russian qualifier Anna Kalinskaya.
In the late match, Eugenie Bouchard went down to China's Lin Zhu 7-5 7-6 (6-3).
The Ukrainian top seed needed three hours to overcome Czech ninth seed Bouzkova 7-5 4-6 6-4 in the decider of the WTA International event.
It marked Svitolina's 14th Tour crown but first since late 2018, when she won the WTA Finals.
Bouzkova, playing her first WTA Tour final, battled hard before falling short against the world number seven.
Svitolina came from a break down to win the opening set before Bouzkova levelled the match by taking the second.
There were five breaks of serve in the final set, with Bouzkova recovering from 4-1 and 5-2 down to get back on serve before getting broken in the 10th game.
Svitolina had not progressed to a semi-final since last year's season-ending WTA Finals, but the Ukrainian ended her drought by defeating 17-year-old sensation Fernandez 6-3 7-5.
World number seven Svitolina needed 98 minutes to book her spot in the final four of the WTA International event in Monterrey on Friday as Arantxa Rus of the Netherlands awaits.
Swedish sixth seed Rebecca Peterson was humbled 6-1 6-1 by Rus in the day's final match.
Number two seed Konta produced a stunning comeback to trump Russian teenager Anastasia Potapova 6-7 (6-8) 6-3 7-6 (9-7).
Konta rallied from 5-2 down in the final set and saved two match points to outlast 18-year-old Potapova in a remarkable encounter in Mexico.
Next up is ninth seed Marie Bouzkova, who beat eighth seed Wang Yafan 6-2 7-5.
Svitolina, the top seed at the WTA International event, crushed Arantxa Rus 6-0 6-1 in just 51 minutes in their semi-final.
The Ukrainian lost just nine points on serve and is yet to drop a set at this year's tournament.
Svitolina is into her 17th WTA Tour final and first of 2020, while she will be aiming for her first title since 2018.
Awaiting her in the decider is Marie Bouzkova, who beat second seed Konta 6-3 6-4.
Bouzkova, the Czech ninth seed, saved all five break points she faced to reach her maiden WTA Tour final.
Svitolina, the top seed at the WTA International event, was too strong for Belarusian Olga Govortsova 6-3 6-4 in one hour, 18 minutes.
The Ukrainian managed four breaks of serve in her victory, moving into a last-eight clash with Canadian teenager Leylah Fernandez.
Konta was pushed more but still got past German Tatjana Maria 7-6 (7-4) 6-3.
The British second seed was wasteful, converting just one of 12 break points to advance.
Russian Anastasia Potapova awaits in the quarter-finals after overcoming Tamara Zidansek 1-6 7-6 (7-3) 6-1.
Arantxa Rus also booked a spot in the last eight thanks to a 7-5 6-0 victory over American 10th seed Lauren Davis.
Li triumphed 7-5 6-1 over third seed Zheng, who held the highest rank of all remaining players after Sloane Stephens and Nadia Podoroska's first-round exits.
World number 52 Zheng struggled to win on her first serve, with Li converted five of seven break points.
American Li, who is ranked 72nd in the world, will next face Swiss qualifier Viktorija Golubic, who beat Russia's Anna Kalinskaya 6-2 6-4.
On the other side of the draw, Canadian Leylah Fernandez defeated Slovakia's Viktoria Kuzmova 7-5 6-3 and will face seventh seed Sara Sorribes Tormo in the other semi-final.
Sorribes Tormo, who is now the highest ranked remaining player, defeated Anna Karolina Schmiedlova 6-3 7-5.
Svitolina won 7-6 (7-3) 3-6 6-2 over the Bulgarian qualifier in two hours and 24 minutes, having trailed 2-0 in the final set, before rattling off the final six games to set up a last-eight meeting with fifth seed Camila Osorio.
The Ukrainian won the title at Monterrey in 2020, with her victory on Thursday maintaining her unbeaten record at the event.
"It was an extremely tough match today," Svitolina said during her on-court post-match interview. "I think Viktoriya played a really good match, and I had to really fight back in the third set to bring back my best game and try to come back in the match.
"In the end, I managed to win six games in a row, so it's a good effort for me. It was an extremely tough first set, second set didn't go my way, and then the third set I was 0-2 down. I was not playing my best, but I was fighting, until the very end.
"And you know, the Ukrainian flag [in the crowd] really helped me today to fight... I was really fighting until the end, and I found my game in the end."
Last week's beaten WTA Abierto Zapopan finalist Marie Bouzkova maintained her good form with a 6-4 6-2 victory over Petra Martic.
Sixth seed Nuria Parrizas-Diaz won 6-4 7-6 (7-2) over Briton Heather Watson, while Wang Qiang defeated Mayar Sherif 6-0 6-7 (2-7) 6-3.
