Third seed Alexandrova claimed a comfortable 6-1 7-5 win in 80 minutes to setup a meeting with Clara Burel, who clinched a surprise 6-3 6-1 win over Varvara Gracheva despite being ranked 56 places below her opponent.
Kristyna Pliskova was knocked out following a hard-fought 7-5 6-4 loss to Alize Cornet.
Cornet's reward is a tie with eighth seed Magda Linette, who triumphed 6-2 6-0 in a one-sided match against Nao Hibino.
Alexandrova is the highest-ranked player remaining in the tournament after top seed Bianca Andreescu withdrew on Tuesday with an abdominal injury.
The world number 33 converted six of her 10 break points to see off Burel 6-3 6-4 in an hour and 10 minutes as she reached her fourth quarter-final of the season, two of those on clay.
Barbora Krejcikova awaits Alexandrova in the last eight after battling back from a set down to beat Caroline Garcia 3-6 6-2 6-1.
Previous Strasbourg champion Garcia held serve throughout the opening set to open up a convincing lead, but Krejcikova did likewise in the second and third sets to advance through.
Number four seed Yulia Putintseva is also into the quarter-finals after Jil Teichmann retired injured when two games down in the opening set.
Arantxa Rus had a walkover win of her own, with French wildcard Harmony Tan a set down when having to withdraw through injury.
Wednesday's other matches also came to an early end because of rain.
Jule Niemeier leads Shelby Rogers 6-4 2-1 ahead of the resumption of that match on Thursday, which is also when Zhang Shuai and Sorana Cirstea will begin their second-round contest – the winner of which will go through to the semis following Andreescu's withdrawal
Andreescu had been absent from the WTA Tour since making the final in Miami back in March, when she was forced to retire when a set and 4-0 down against Ashleigh Barty due to an ankle injury.
A positive COVID-19 test result ruled her out of competing in Madrid and also Rome, though the Canadian showed few signs of rust on her return.
The top seed defeated the world number 279 – who was making her main-draw debut after coming through qualifying – in just 61 minutes, a 6-1 6-2 triumph sealed in a hurry thanks to five breaks of serve.
Champion at the 2019 US Open, Andreescu did not play in any grand slam event last year. She has only featured in the main draw at the French Open once before, reaching the second round at Roland Garros two years ago.
"I feel really, really good," the world number seven said after an impressive opening display. "I had really good preparation coming into this tournament, so I'm super happy."
Also in action on Monday, Yulia Putintseva overcame Sweden’s Rebecca Peterson via a tie-break in the deciding set of their see-saw contest.
The fourth seed eventually prevailed 6-4 3-6 7-6 (7-2) after three hours and 20 minutes on court, booking her a spot in the last 16 of the tournament.
Zhang Shuai was successful in her first outing, beating Misaki Doi 7-5 6-4. Barbora Krejcikova was another seed to make it through, having led 6-3 3-0 when opponent Oceane Dodin retired.
Caroline Garcia overcame Zarina Diyas 7-5 6-2, while Maryna Zanevska needed less than an hour to overcome Yuliya Hatouka 6-2 6-1 and set up a clash with Andreescu.
Jil Teichmann was also a winner in straight sets against Anna Blinkova, but Venus Williams' campaign is over early after going out to Sorana Cirstea, who dominated a decider to triumph 6-1 2-6 6-1.
Until this week the Canadian had been absent from the WTA Tour since making the final in Miami back in March, missing recent events after a positive COVID-19 test.
But she has now won two straight matches on clay for the first time in her career, having barely played on the surface at tour level before.
Top seed Andreescu was playing an opponent ranked outside of the world's top 250 for a second straight day, though she emphatically did the job against qualifier Zanevska, winning 6-1 6-4 in just 65 minutes.
Aside from needing to recover from 4-2 down in the second set, Andreescu had few problems and converted all five of the break points she forced in the contest.
However, the second seed at the WTA 250 event is out.
Australian Open quarter-finalist Jessica Pegula was upset by Arantxa Rus, losing 6-4 6-4.
Pegula won only 10 of her 31 points on second serve as she was broken on five occasions.
But there was relief for seventh seed Shelby Rogers, who won an epic contest lasting three hours and 23 minutes against fellow American Christina McHale.
Rogers won 7-5 6-7 (6-8) 7-5 in a memorable clash. The eventual winner was a point away from wrapping up the victory in straight sets before later needing to save a match point herself in the decider.
Romanian Cirstea emphatically beat eighth seed Zhang Shuai 6-2 6-1 and moved into the last four after Bianca Andreescu withdrew following her second-round success over Maryna Zanevska due to an abdominal injury.
Cirstea lost only seven of the 31 points on her first serve and did not face a solitary break point in an impressive victory ahead of the French Open.
She broke Zhang on four occasions and will do battle with Magda Linette for a place in the final.
Linette took out fourth seed Yulia Putintseva 6-3 6-3, breaking once in the first set and three times in the second.
Qualifier Niemeier upset seventh seed Shelby Rogers, completing a 6-4 7-6 (8-6) victory following a rain delay.
The German will look to pull off another surprise when she faces Barbora Krejcikova, who eliminated Ekaterina Alexandrova with a 7-6 (7-4) 6-1 victory.
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.
World number 81 Juvan knocked off world number eight Pliskova 6-2 7-5 in just one hour and 26 minutes.
Speaking afterwards, the 21-year-old said: "This whole year, I feel like I've been so close to beating these players.
"I was like, 'OK, let's go for it, let's be aggressive, I can do it, I'm always so close.'
"We prepared well, and I think I stuck to being aggressive and trying to make the points, not just waiting for her, and that worked at the end.
"I felt like I was really fast, and I felt really strong, so I wasn't too worried if it's going to go to the third set, if it's going to be a long match. I relaxed and tried to stick to my plan, because I thought at the end it's going to be worth it, no matter what happens."
Juvan will face three-time grand slam champion Angelique Kerber in the final.
Kerber won the first set of her semi-final against Oceane Dodin on a tie-break and broke in the opening game of the second before her opponent retired.
At the Grand Prix Sar La Princesse Lalla Meryem in Rabat, Martina Trevisan beat fellow Italian Lucia Bronzetti in straight sets to book a final with Claire Liu, who won without hitting a ball as fifth seed Anna Bondar withdrew because of a shoulder injury.
World number 22 Kerber rolled back the years with a battling 6-2 4-6 6-4 victory in a time of a little over two hours on Thursday.
She converted four of her nine break points and will now face the unseeded Oceane Dodin, who needed just an hour to overcome Viktorija Golubic 6-3 6-0.
Top seed Karolina Pliskova continued her progression with a 6-4 7-6 (8-6) victory over Maryna Zanevska, meanwhile, and will take on Kaja Juvan for a place in the final after she beat fourth seed Elise Mertens 7-6 (7-3) 6-4.
Pliskova, who saved four set points in the tie-break, is aiming to become the fourth Czech champion in Strasbourg.
At the Grand Prix Sar La Princesse Lalla Meryem, Anna Bondar is the last seed standing after opponent Ajla Tomljanovic retired injured when 5-1 down in the opener.
Clair Liu saw off Astra Sharma 6-4 6-1 to reach the semi-finals in Morocco, while Lucia Bronzetti and Martina Trevisan will meet in the other final-four showdown.
Bronzetti outlasted third seed Nuria Parrizas-Diaz 6-1 3-6 7-6 (7-5) while Liu beat Astra Sharma 6-4 6-1.
World number 38 Krejcikova lost to Garbine Muguruza in the Dubai Tennis Championships final in March but suffered no such disappointment this time around, overcoming her Romanian opponent in one hour and 41 minutes.
Cirstea was in fine form this week following her Istanbul success, but the world number 61 was on the back foot from the off after losing her first two service games, offering up six break points in the process as Krejcikova reeled off four games in a row.
Krejcikova squandered two set points as Cirstea broke back, but the Czech took the lead at the third time of asking.
Cirstea rallied straight away in the second set, yet problems on her own serve continued as she suffered successive breaks and those errors ultimately handed Krejcikova an advantage she did not relinquish, with the 25-year-old sealing her maiden title with a powerful cross-court forehand.
Handed a quarter-final walkover due to the withdrawal of top seed Bianca Andreescu due to injury earlier in the week, Cirstea fell behind to Poland's Magda Linette on Friday, but hit back to win 3-6 6-4 6-2.
Cirstea, world number 61, is in the hunt for her second title of the season after her success in Istanbul last month – a trophy that ended a barren run of over 12 years for the Romanian.
The 31-year-old will face stern competition from fifth seed Krejcikova, however.
Krejcikova is in the hunt for her maiden Tour-level triumph, after falling short at the final hurdle in Dubai in March.
She too needed three sets to claim a place in the final, with world number 216 Jule Niemeier pushing Krejcikova all the way.
However, the Czech – ranked at 38th in the world by the WTA – rallied after losing the first set 7-5.
Having clinically taken the three break points on offer to her in set two, Krejcikova broke for a final time to make it 4-3 in the decider – a lead she would not relinquish as she prevailed 5-7 6-3 6-4.
Having endured an injury-hit season to date, world number eight Pliskova made the perfect start to her campaign in France with a routine 6-4 6-2 win over Ukrainian 19-year-old Marta Kostyuk.
Kerber, who is only missing a victory at the French Open – which begins later this month – to complete a Career Grand Slam, overcame teenager Diane Parry 6-3 6-4 in her opener, setting up a round-of-16 clash with world number 45 Aliaksandra Sasnovich.
Some of the other big names participating in Strasbourg, however, were not so lucky, with 5th and 6th seeds Shuai Zhang and Sloane Stephens crashing to first-round exits.
Shuai went down 6-2 6-3 to Belgium's Maryna Zanevska and Stephens capitulated to a 2-6 6-4 6-1 loss to Nefisa Berberovic, while Heather Watson set up a last-16 meeting with eighth seed Magda Linette by beating Katharina Hobgarski 6-4 6-1.
Meanwhile, Garbine Muguruza made a winning start to her campaign at the Grand Prix Sar La Princesse Lalla Meryem in Morocco, as the world number 10 builds towards a tilt at French Open glory having triumphed at Roland Garros back in 2016.
Muguruza had few difficulties in beating Anna Danilina 6-3 6-2, and will face Martina Trevisan in the round-of-16 after the Italian beat China's You Xiadoi 6-0 6-4.
Third seed Nuria Parrizas-Diaz had to come through a more difficult challenge in Rabat, overcoming Carol Zhao 7-6 (7-4) 1-6 6-2, while eighth seed Anna Kalinskaya was the highest-ranked player to fall at the first hurdle, going down 6-3 6-7 (5-7) 6-3 to Lucia Bronzetti.
The Kazakh beat Nao Hibino 6-3 6-4 in one hour and 16 minutes in the last four to reach her first final since the Tour resumed following the coronavirus pandemic.
No one has been to more WTA finals in 2020 than Rybakina, though she has only won one of her previous four - the Hobart International in January.
Hibino had knocked out Sloane Stephens and Jelena Ostapenko to reach her maiden clay-court semi-final, but this proved a step too far for the unseeded Japanese.
Svitolina made her second final of 2020 with a 6-2 4-6 6-4 triumph over Aryna Sabalenka in the other last-four meeting.
Sabalenka had completed her rain-delayed quarter-final over Katerina Siniakova across three sets earlier in the day, and that may have taken its toll in a match against Svitolina that lasted almost two hours.
Number four seed Sabalenka was in fine form as she made a convincing start to her campaign, taking just over an hour to beat qualifier Perez 6-4 6-3 and move into the second round.
Perez was last year's doubles champion in Strasbourg but was no match for the world number 12, who is currently operating with her hitting partner as a coach.
Sabalenka had been working with Kindlmann, who used to coach her doubles partner Elise Mertens, heading into the US Open, but the Belarusian elected not to keep him on.
"I told him that I think I'm not ready for a new person on my team," Sabalenka explained.
"He's a great guy, great coach, but I'm just not ready. I'm going to work with my hitting partner for now as my coach."
Anna Blinkova, who beat Myrtille Georges 6-1 6-2, awaits Sabalenka in round two.
Former US Open champion Sloane Stephens succumbed to the shock result of the day, meanwhile, as she crashed out to world number 83 Nao Hibino.
Stephens was going up against an opponent who was 0-3 across her first three events since the season was restarted, but Hibino secured a hard-fought 6-2 3-6 6-1 triumph.
"Last week, I lost in qualies in Rome and it was not a good match, so I learned from that," Hibino said after the match. "Of course, Sloane is a good player, especially on clay courts. I prepared mentally and with tactics, so I think it helped a lot today."
It was a bad day for Stephens' compatriot Christina McHale, who went down 6-7 (4-7) 7-5 7-6 (7-3) to Zarina Diyas.
Magda Linette beat Pauline Parmentier to set up a tie with second seed Elina Svitolina, while third seed Kiki Bertens will meet Jelena Ostapenko.
There were also victories for Elena Rybakina, Ekaterina Alexandrova, Alize Cornet, Shuai Zhang and Katerina Siniakova.
The world number 12, this year's champion in Doha, made the last-eight stage for the first time since the WTA returned after the coronavirus shutdown having won just three matches before this week.
Katerina Siniakova awaits after the Czech upset the odds to defeat seventh seed Ekaterina Alexandrova 6-2 6-4.
Alexandrova defeated Siniakova when winning her first WTA singles title in Shenzhen this season but was unable to repeat the feat.
"I feel really good on clay," Siniakova said. "It was tough, it was a good match, I'm happy about it."
Nao Hibino defeated Zarina Diyas in straight sets, while third seed Kiki Bertens withdrew injured when trailing 4-2 in the decided set of her clash with Jelena Ostapenko.
The second seed won the first set via a tie-break and came back from a double break down in the second to seal a 7-6 (7-0) 7-5 victory in an hour and 58 minutes.
Linette was just two points away from winning the opener and missed an opportunity to force a decider on set point in the second.
"It definitely was not easy. She was fighting back, she was trying to produce a good level; I was up and down," said Svitolina, who reached the quarter-finals on her return to the WTA Tour at the Internazionali d'Italia last week.
"It's not easy to come from another tournament with different balls, different conditions. I was trying just to fight and, in the end, I was lucky I finished in two sets."
Jil Teichmann awaits Svitolina in the last eight following a 7-6 (7-3) 7-5 win against 2018 champion Anastasia Pavlyuchenkova, while there were also victories for Elena Rybakina and Zhang Shuai.
Number two seed Svitolina was made to work hard for her 6-4 6-3 victory over Jil Teichmann, battling back from a break down in both sets.
The world number five took an hour and 23 minutes to secure her first semi-final for six months.
"It was a great fight from Jil and I think both of us were playing at a really good level at some points," Svitolina said.
"I was fighting. I didn't start the match very well, but I was trying to be very focused and fight back. In the end, I'm very happy with how I handled the match."
Sabalenka and Siniakova will resume their contest on Friday after the latter claimed the first set 6-2. Play was suspended due to rain with the Czech 2-1 down in the second but serving next.
The other semi-final will be contested by fifth seed Elena Rybakina, who defeated Zhang Shuai 6-3 6-2, and Nao Hibino, who ousted 2017 French Open champion Jelena Ostapenko 7-6 (7-2) 7-6 (7-4).
The Ukrainian was a 6-4 1-6 6-2 winner against Kazakhstan's Elena Rybakina in Saturday's final.
In a title match that was delayed for a short while because of rain, Svitolina was delighted to find focus for the decider after momentum looked to be with Rybakina.
Searching for the form she displayed early on in the match, Svitolina saved a string of break points in the opening game of the third set, restoring the belief that had been ebbing away.
The world number five said: "It really gave me confidence to come back into the match. The second set was a little bit one-sided. It gave me hope and a better feel at the beginning of the third set."
Svitolina, who won the French Open girls' title in 2010 when she beat Ons Jabeur, has twice reached quarter-finals in the main draw in Paris.
She has a strong record on clay though, twice winning the Internazionali d'Italia at the expense of Simona Halep, beating the Romanian in the 2017 and 2018 finals in Rome.
Her strike rate in WTA finals is also phenomenal, with Svitolina improving her record to 15 wins from 18 title matches.
The 26-year-old described her third-set revival as "really positive stuff for me", as it showed she could cope with the unusual circumstances.
Clay-court tennis in Europe is typically played during the warmest months of the year, but the COVID-19 pandemic has shunted it back, and the soggy Strasbourg weather may be a sign of things to come in the year's final grand slam.
Svitolina, quoted on the WTA website, said: "Normally the tournaments are playing in really hot conditions. We were happy to finish today. In the end we got lucky to play."
As Svitolina enjoyed her second title of the year, Rybakina reflected on a fourth defeat in five WTA finals in 2020.
Rybakina said: "I can serve a little bit better and make some better decisions. It was so tough to play today because of the cold."
Pavlyuchenkova, champion at Strasbourg in 2018, overcame Van Uytvanck 6-3 7-5 on Sunday in a contest lasting an hour and 37 minutes.
The world number 36 had to save two set points in the 10th game of the second but held her nerve and quickly wrapped things up without the need for a decider.
With a limited number of fans allowed to attend sporting events in France amid the coronavirus pandemic, Pavlyuchenkova was thrilled to finally be back playing in front of spectators.
"I like this event and I have good memories as I won it two years ago," she said. "It was strange and nice at the same time to see a crowd out there today. There were a lot of people.
"I'm really happy with the win and the way I played. I started the match really well. I was aggressive and solid at the same time."
Jil Teichmann is next up for Pavlyuchenkova after her 6-2 6-3 triumph over sixth seed Amanda Anisimova.
In Sunday's other match, Clara Burel came from behind to beat Kateryna Bondarenko 3-6 6-1 6-4.
Second seed Tomljanovic wrapped up a 6-2 6-1 win over her Spanish opponent in Rabat on Sunday, kick-starting her bid to better her second-placed finish at the 2018 edition of the event.
The world number 44, who was beaten by fellow Australian Ashleigh Barty in the Wimbledon quarter-finals after overcoming Emma Raducanu in London last year, is on course for a potential meeting with Croatian 16-year-old Petra Marcinko, who shocked ninth seed Rebecca Peterson to claim a three-set victory.
The Australian Open girls' champion and junior world number one claimed a superb 6-0 2-6 7-5 win over the Swede for her first career top 100 triumph.
At the Internationaux de Strasbourg, meanwhile, eighth seed Linette saw off Varvara Gracheva 6-3 6-0 to reach the round-of-16, setting up a potential tie with Heather Watson.
Elsewhere, Harmony Tan downed Australia's Samantha Stosur 6-2 6-1 to set up a potential round-of-16 meeting with Shuai Zhang, who faces Belgium's Maryna Zanevska on Monday.
Second seed Tomljanovic was a 7-5 6-2 victor against Anna Karolina Schmiedlova, reeling off the last four games in succession to advance in Morocco.
Fellow Australian Astra Sharma joined her in the last eight by overcoming wildcard Petra Marcinko 5-7 6-3 6-3.
Kristina Mladenovic had to save a match point after passing up two herself to finally get over the line with a 6-3 3-6 7-6 (9-7) success - her first singles win of the year - over lucky loser Tessah Andrianjafitrimo in a first-round clash.
At the Internationaux de Strasbourg, third seed Cirstea stormed to a one-set advantage against Ekaterina Makarova but soon fell away and succumbed to a 1-6 6-3 6-2 loss.
Magda Linette breezed past Heather Watson 6-1 6-1 to reach the quarter-finals, where she was joined by Maryna Zanevska after the Belgian's 4-6 7-5 6-1 comeback win against Harmony Tan.
Top seed Karolina Pliskova awaits American Bernarda Pera who defeated Elena-Gabriela Ruse in straight sets, while Anna-Lena Friedsam will take on Elise Mertens after rallying to beat Daria Saville 4-6 6-3 7-6 (7-5).