Sabalenka, playing in her first event since claiming a maiden grand slam title in Melbourne, recovered from falling behind in style to win 2-6 6-1 6-1 on Wednesday.
Ostapenko won the tournament last year and looked to be in with a chance of extending her winning streak in Dubai to seven matches.
But Sabalenka launched a strong recovery to reach the quarter-finals and extend a stunning run to start the season to 13 consecutive wins.
The second seed tightened up her game in the second and third sets and will face either Petra Kvitova or Barbora Krejcikova in the last eight.
Sabalenka had been broken three times by Ostapenko in the opening set, but she only had to fend off one break point from there.
"In the first set, she played unbelievable tennis and I couldn't do anything," Sabalenka said.
"I was looking at my team asking like, 'What can I do?', but somehow, I turned around this game and started playing really incredible tennis.
"She plays really fast, deep balls, and I tried to stay super low, stay focused, and try to put more balls in than she did. I'm so happy that I did it."
A lower back injury for Wimbledon champion Elena Rybakina robbed supporters of what had looked like being a thrilling matchup against Coco Gauff.
The withdrawal of Rybakina meant Gauff progressed via a walkover and will face fellow American Madison Keys next.
Keys and Gauff have played twice before, winning one match apiece.
It was Gauff who won their most recent encounter in the third round of the US Open last year.
Top seed Iga Swiatek had earlier booked her place in the last eight, with the Pole's latest dominant showing in Dubai earning praise on social media from Andy Murray.
And news followed that Karolina Pliskova, her semi-final opponent, had been forced to withdraw.
Swiatek benefited from a walkover in the quarter-finals en route to winning the Qatar Open last week and is now only two wins away from another title.
Two-time Wimbledon champion Kvitova, the 12th favourite in the United Arab Emirates, eased past Italy's Martina Trevisan 6-2 6-1 to make a dominant start.
World number 15 Samsonova was made to work to beat Paula Badosa, winning 6-7 (3-7) 7-6 (7-5) 6-4 to tee up a clash with Qinwen Zheng, who overcame compatriot Zhang Shuai in straight sets.
Samsonova's triumph took three hours and 22 minutes, the longest match of the WTA Tour season thus far, in a thrilling first-round encounter between two top-20 players.
"Playing against Paula is always tough," 14th seed Samsonova said in her on-court interview. "She's doing unbelievable, so I'm really proud that I stayed on the court until the end.
"I think I'm growing match after match, day by day. I know it's a long journey, and I hope to continue like that."
Barbora Krejcikova, the 2021 French Open champion, cruised into the last 32 with a comfortable 6-4 6-2 victory over Irina-Camelia Begu as she aims to go one better than her runners-up finish two years ago in Dubai.
Another routine victory saw American Madison Keys ease past Jasmine Paolini 6-1 6-1, but there was no such luck for 2020 Australian Open champion Sofia Kenin.
She was dispatched 6-1 6-1 by world number 26 Marie Bouzkova, while Amanda Anisimova claimed a 6-3 6-2 win over veteran two-time grand slam finalist Vera Zvonareva.
Viktoriya Tomova had too much for Kaia Kanepi in a 6-3 6-1 success, with her reward a second-round clash against third seed Jessica Pegula.
World number four Pegula lost to the in-form Iga Swiatek in the Qatar Ladies Open final on Saturday, and Leylah Fernandez will face the Pole next after beating Julia Grabher 6-4 6-2.
The third seed struck 26 winners en route to a 7-5 6-4 triumph on Thursday, but it was his serve that pleased him most.
Shapovalov, ranked 12th in the world, sent down 10 aces as Frenchman Chardy was deprived of any break-point openings.
"I've focused on my serve a lot in the past couple of weeks," the Canadian said.
"I have worked on placing it and tried out different types of serves to have more variation. I hope I can continue that.
"I've also worked on my footwork and positioning during rallies. I am feeling the ball well on both sides. If I am moving well, everything goes into place."
Harris was a surprise winner over Kei Nishikori, sealing a 6-1 3-6 6-3 success to dump out the former world number four.
Second seed Andrey Rublev defeated Marton Fucsovics 7-5 6-2 and will now face fellow Russian Aslan Karatsev.
Wildcard Karatsev continued his run with a hard-fought victory over teenager Jannik Sinner, coming from a set down in a 6-7 (5-7) 6-3 6-2 win.
The 19-year-old rising star, who won the Great Ocean Road Open last month, prevailed in a match that remained in the balance until the end on Wednesday.
Sinner won 6-4 3-6 7-5 to reach the quarter-finals, with Bautista Agut following top seed Dominic Thiem - who lost in the second round - out of the tournament.
After hitting 16 aces, Sinner – the youngest player in the ATP Tour top 100 – will face surprise Australian Open semi-finalist Aslan Karatsev next.
Second seed Andrey Rublev is through after a comfortable 6-3 6-1 win over Taylor Fritz.
Rublev will face Marton Fucsovics, who ousted Serbian Dusan Lajovic in three sets, in the last eight.
The Russian now has 22 consecutive wins at ATP 500 events, a run that has included four titles at that level. Only Roger Federer has ever recorded a longer streak, doing so with a run of 28 between 2014 and 2016.
"I am really happy that I can win in straight sets and quite confidently," Rublev said.
"I know Taylor since [the] juniors and it is always tough to play against him, because he has a huge serve and he is playing really fast.
"The first set was not even rallies because everything was serve, winner or serve, mistake, so everything was so fast.
"In these conditions, it is tough to find the rhythm. You don't know what's going to happen and it's really not easy, but I'm happy that in the end I made it."
Third seed Denis Shapovalov is also through after a 6-4 6-3 win over Hubert Hurkacz, the Canadian booking a last-eight meeting with Jeremy Chardy.
Kei Nishikori will play Lloyd Harris in the other quarter-final.
After losing the first set, the world number 10 staved off defeat in a nerve-wracking second-set tie-break.
The fourth seed clung on as Davidovich Fokina saw a trio of opportunities to clinch a shock win go begging, the Spaniard made to pay as his Italian counterpart fought back to prevail 4-6 7-6 (8-6) 6-3.
Sinner, who will next face former world number one Andy Murray, said: "It was a very tough match. I know him, but we've never played against each other.
"It was the first time for both of us and it was a tricky one, saving three match points. On the first one I got lucky because it was out, but not so far [out]."
Second favourite Andrey Rublev won both the singles and doubles titles in Marseille last week and continued his fine form with a 6-4 7-5 win over Daniel Evans that saw the Russian send down 28 winners.
Sixth seed Denis Shapovalov had to recover from a set down to see off Marton Fucsovics, though fifth seed Hubert Hurkacz enjoyed a more routine straight-sets triumph over Alexander Bublik.
Eighth seed Roberto Bautista Agut made relatively light work of Arthur Rinderknech but defending champion and seventh seed Aslan Karatsev was stunned 7-5 6-3 by Mackenzie McDonald.
Karen Khachanov needed a little shy of three hours to beat Alex de Minaur, his dubious reward a second-round clash with Novak Djokovic as the world number one continues his return to the Tour following his controversial Australian Open absence.
It only took 76 minutes for the number one seed to record a 6-1 6-0 triumph on Wednesday, continuing a fine run after her triumph in Qatar last week.
Swiatek had only narrowly beaten Samsonova in an epic three-set encounter in the Stuttgart semi-finals last year, but was completely dominant this time around at the WTA 1000 event.
Samsonova struggled in recording a first-serve percentage of just 58.5, and Swiatek was ruthless in winning 19 of 22 points on the Russian's second serve.
Swiatek did not even have to fend off a break point in cruising to victory and will play Karolina Pliskova in the quarters.
Pliskova, the two-time grand slam finalist, battled to a 7-5 6-7 (6-8) 6-2 win over Anhelina Kalinina to reach the last eight in Dubai for the fifth time in her career.
There were also two American successes, with Madison Keys needing only 57 minutes to beat Victoria Azarenka, who appeared to be struggling with her movement.
Keys had lost all of her previous four meetings with Azarenka but triumphed 6-2 6-1 in routine fashion.
And Jessica Pegula joined her compatriot in progressing, winning her first career meeting with Ana Bogdan in straight sets.
Elsewhere, 2019 winner Belinda Bencic crashed out, with Karolina Muchova, who also knocked out Maria Sakkari this week, triumphing 6-1 6-4 to book a quarter-final date with Pegula.
The world number one cruised to a 6-1 6-1 triumph over 2021 US Open finalist Leylah Fernandez, just three days after winning the Qatar Ladies Open in Doha.
That marked Swiatek's 41st main-draw victory in WTA 1000 events in just her 53rd outing, only Serena Williams and Maria Sharapova (52 each) have won more than 40 such matches in fewer attempts.
The 21-year-old has won her last 35 hard-court matches against opponents ranked outside the world's top 30, though Swiatek said she had to adapt against Canada's Fernandez.
"It wasn't that easy for sure. It was much tougher than the score said," said Swiatek, who will look to make the fourth round for the first time in Dubai when she faces Liudmila Samsonova.
"In the second set... I needed to go a level up. I didn't have much time to get used to the conditions, but I'm just happy I could play solid tennis."
Jessica Pegula, the third favourite at the tournament, defeated Viktoriya Tomova 6-2 5-7 6-1 to set up a third-round battle with Ana Bogdan, who overcame Shelby Rogers 7-6 (7-3) 6-3.
Fifth seed Coco Gauff coasted past Aliaksandra Sasnovich with a 6-0 6-4 victory, teeing up a meeting with Elena Rybakina, who slammed six aces in a 7-5 6-2 defeat of Marie Bouzkova.
World number two Aryna Sabalenka, who defeated Rybakina at this year's Australian Open final, made light work of lucky loser Lauren Davis in a straight-sets rout as she claimed her 12th straight win in 2023.
Dubai's defending champion Jelena Ostapenko will be the next challenge for Sabalenka after defeating 17-year-old Linda Fruhvirtova for her seventh straight win at the event.
Barbora Krejcikova saved four match points en route to a 6-4 4-6 7-5 win over seventh seed Daria Kasatkina and will meet Karolina Pliskova next after she downed sixth favourite Maria Sakkari in straight sets.
Belinda Bencic and Marta Kostyuk played out the match of the day as the former claimed a 6-7 (7-9) 7-6 (7-5) 6-4 triumph, with that clash taking three hours and 27 minutes – the second-longest on the WTA Tour this year.
Sabalenka fought back from a set down to end the title defence of Jelena Ostapenko a day earlier, but she came up short against Barbora Krejcikova as her Czech opponent overcame a tough first set to run out a 0-6 7-6 (7-2) 6-1 victor.
Sabalenka, playing in her first event since claiming a maiden grand slam title in Melbourne, romped into the lead by breaking Krejcikova's serve three times to go a set ahead.
But the world number two was pegged back in the second as Krejcikova battled to force a tie-break, which she dominated to level the match.
Krejcikova then completed the shock victory in style, breaking the second seed twice in the final set before clinching the win on her third match point to end Sabalenka's run of 13 straight triumphs.
Karolina Muchova's withdrawal due to an abdominal injury means it is Jessica Pegula who will face Krejcikova in the semi-finals on Friday.
After Swiatek reached the final four by virtue of Karolina Pliskova pulling out because of an illness, Gauff set up a sixth meeting with the world number one by beating Madison Keys 6-2 7-5.
In those five previous clashes between the pair, Gauff is yet to win a set.
But after cruising past Keys, doing so by converting four of five break points and winning 90 per cent of her service games, Gauff is confident of improving her dismal record against Swiatek on Friday.
"All five times, I did something wrong," Gauff said. "To be honest, she's playing great tennis and there's a reason she's world number one.
"Tomorrow I have no pressure. I just have to play my game. I definitely think I've gotten better since the last time I played her.
"Ranking is just a number at the end of the day. You just have to step on the court believing you can win, and that's what I'm going to do tomorrow."
The unseeded Halep, who was champion in 2020, needed just an hour and 11 minutes to see off Alison Riske 6-2 6-4 as she looks to climb back up the rankings.
The two-time grand slam winner went into this week ranked 23rd in the world after a difficult 2021 that was ravaged by injury, but she was in fine form against Riske. She showed good spirit to dig herself out of a hole in the second set and save two break points – the American's only ones in the entire match – in the fourth game.
Swiatek, seeded sixth, was even more comfortable against Daria Kasatkina, defeating the Russian 6-1 6-2 in just 65 minutes.
Kasatkina had no answer to Swiatek in the first set and, by the time she started to gain some form of momentum, she was already a set and a break down.
Swiatek had few issues closing out the match and was joined in the second round by Petra Kvitova, who dropped just two games en route to an emphatic 6-2 6-0 defeat of Camila Giorgi.
Krejcikova was the highest seed in action. The Czech, who lost to Garbine Muguruza in last year's final, was given a tougher examination than some of her rivals, with wildcard Caroline Garcia putting up a solid fight.
Krejcikova came through 6-4 7-6 (7-0) in the end, blowing the Frenchwoman away in the second-set tie-break, though she will surely have to sharpen up if she is to go one better than 2021 – the 26-year-old hit just 12 winners to 28 unforced errors.
There was also a victory for Jessica Pegula in an all-American affair with Coco Gauff that included 10 breaks of serve – the former won 6-4 6-4.
The 18-year-old beat Swiss opponent Viktorija Golubic 6-4 6-1 in a final contested by two qualifiers, achieving her breakthrough win in an hour and 29 minutes.
Golubic saved five match points but eventually was put away by Tauson, who has spent most of her senior career to date on the second-tier ITF tour.
She caused a major shock at the French Open in September by beating US Open semi-finalist Jennifer Brady in the first round, and Tauson should now become a more familiar presence at the higher level.
The win carries the youngster into the WTA top 100 for the first time, and it completed an impeccable trip to France that saw Tauson win all seven of her matches, including two qualifying rounds, in straight sets.
She said of her performance: "I think I've been really solid; especially after the first set, I've come out good in every single match."
Quoted on the WTA website, Tauson added: "I just kept my game going. It's been a weird week like that, normally I have some fall-outs, but I haven't had any of those this week, so I'm very happy with that."
Tauson shocked Russian top seed Ekaterina Alexandrova in the first round at the start of the week in Lyon, and Alexandrova lost to another teenager on Sunday as the Dubai Tennis Championships began.
The world number 33 was handed a tough draw against American Coco Gauff, who scraped through 7-6 (7-3) 2-6 7-6 (10-8) in a match lasting two hours and 41 minutes.
Gauff served 12 double faults, including seven in the deciding set, but found a way through to the second round.
Svetlana Kuznetsova, Ons Jabeur and Alize Cornet were among the other winners on day one. The top eight seeds, who include Iga Swiatek, Karolina Pliskova, Elina Svitolina and Petra Kvitova, have all received byes to round two of the WTA 1000 event.
The reigning US Open champion, given a bye for the first round, lost 6-3 6-4 to his South African opponent, who sits 77 places further down the ATP rankings.
The Austrian has endured a difficult start to 2021. He lost in straight sets to Grigor Dimitrov in the last 16 of the Australian Open and was beaten by Roberto Bautista Agut in the quarter-finals in Doha.
It was a first win over a top-five player for Harris, who was not once taken to deuce on serve during their 72 minutes on court.
"I'm super, super happy with that win. [He is] by far the highest-ranked player I have beat," said Harris. "I look up to Domi a lot so, for me, it is a special feeling. I am really happy. Just the fact that I am playing good tennis, match in, match out now is giving me a lot of confidence.
"I was serving really well. I don't think I faced any break points. I took control of those games and [in] one or two games on his serve, I gave myself a good look. I played some of the important points very well. I am very proud of that."
While Thiem is struggling for form, things are looking far better for Andrey Rublev, who beat Emil Ruusuvuori 6-4 6-4 to stretch his winning streak at ATP 500 events to 21 matches.
The world number eight, who will face Taylor Fritz in the next round, equalled Andy Murray for the second-best winning run at this level of the Tour. Roger Federer (28) holds the record.
Third seed Denis Shapovalov beat Jan-Lennard Struff for the loss of just four games, while Bautista-Agut advanced after opponent Matthew Ebden retired in the first set.
Fifth seed David Goffin was beaten in straight sets by Kei Nishikori, who recorded just his third victory of the year.
Karen Khachanov and Jannik Sinner each advanced after three-setters, while Marton Fucsovics and Aslan Karatsev were also taken the distance before progressing.
Hubert Hurkacz, Lorenzo Sonego, Dusan Lajovic, Aljaz Bedene and Filip Krajinovic also won on Tuesday.
Djokovic, whose decision not to be vaccinated against COVID-19 caused him to be deported from Australia on the eve of the year's first grand slam, eased to a 6-3 6-3 win over Lorenzo Musetti in his first match and made similarly light work of Karen Khachanov on Wednesday.
The world number one has won in Dubai on five occasions, last doing so in 2020, having elected against defending his title last year.
However, the Serbian is looking good to regain the crown in what is his first tournament on the ATP Tour in 2022, after he was unable to feature in Melbourne.
Djokovic needed 98 minutes to see off Khachanov 6-3 7-6 (7-2) and tee up a quarter-final tie against qualifier Jiri Vesely.
"I missed it [playing competitively]. This is my life," Djokovic said, with his previous competitive appearances coming in the Davis Cup Finals in November and December.
"This is what I have known for the past 20 years. Tennis is my love. I enjoy bringing positive energy and memories for people who watch."
It was not all plain sailing for Djokovic, who offered up four break points, but the 34-year-old clawed back three of them.
"I was feeling excited and motivated," added Djokovic, who has progressed to the quarters in Dubai every time he has featured at the tournament.
"But also at the same time I was feeling stressed. Particularly at the moments when I was facing break points. I thought the atmosphere in the stadium was terrific."
Djokovic, who will lose his place at the top of the ATP rankings if Daniil Medvedev triumphs in Acapulco, should have little trouble in sealing a semi-final spot, though Vesely does come into that tie on the back of a surprise 6-2 6-4 win over world number 15 Roberto Bautista Agut, who had triumphed in Doha last week.
Murray falls short of landmark win
Second seed Andrey Rublev came from a set down to defeat Kwon Soon-woo 4-6 6-0 6-3, and will go up against American Mackenzie McDonald for a place in the last four.
There was no such joy for former world number one Andy Murray, however, who fell to Jannik Sinner 7-5 6-2.
"It is a special feeling [to share the court with Murray]," said Sinner, who will next face Hubert Hurkacz, a 6-3 6-2 winner over Alex Molcan.
"He is a legend. Winning three grand slams, many, many tournaments and he has had some unfortunate moments with surgeries. His fighting spirit is incredible.
Murray was chasing a 700th tour-level win of his career but failed to muster a single break opportunity against the Italian, who made it to the quarter-finals in Melbourne last month.
Belarusian Sabalenka made light work of 19-year-old Marta Kostyuk, sealing a 6-4 6-1 win in one hour and 15 minutes.
Standing in her way of a third consecutive quarter-final in Dubai is Petra Kvitova, who beat Camila Giorgi on Monday.
Last year's champion and fourth seed Muguruza began her title defence with a 7-6 (7-5) 2-6 6-2 win over Czech qualifier Katerina Siniakova in two hours and 24 minutes.
Spaniard Muguruza will face Veronika Kudermetova in the second round after the Russian beat former world number one Victoria Azarenka in straight sets earlier on Tuesday.
There were also wins for eighth seed Ons Jabeur and 10th seed Elina Svitolina against Vera Zvonareva and Mayar Sherif respectively.
Elsewhere, there was a shock as qualifier Elena-Gabriela Ruse dumped out third seed Paula Badosa 6-3 5-7 6-4.
Ninth seed Danielle Collins is also out after the American retired due to dizziness in the second set against Marketa Vondrousova.
Sofia Kenin failed to put up a fight as she went down 6-1 6-2 to Jelena Ostapenko.
Tsitsipas claimed his first title of the season by retaining his Open 13 Marseille on Sunday and saw off Carreno Busta 7-6 (7-1) 6-1 two days later.
The second seed put the Spaniard under pressure with rasping returns and was broken just the once to set up a meeting with Alexander Bublik.
Paire saved four match points in a 2-6 7-5 7-6 (7-1) win over 2014 US Open champion Cilic and will face compatriot Richard Gasquet in round two.
Cilic knocked the Frenchman out of the Australian Open in the second round last month, but fell at the first hurdle in the United Arab Emirates.
Paire had lost five consecutive matches against the powerful Croatian, including a five-set battle at Melbourne Park, yet he fended off two match points in the second set and as many in third before bossing a decisive tie-break.
World number 37 Dan Evans claimed the scalp of fourth seed Fabio Fognini, winning 3-6 6-4 7-5 on day two of the tournament.
Fifth seed Roberto Bautista Agut was another to suffer a surpise exit as he went down 7-6 (7-2) 7-5 to Jan-Lennard Struff.
Yasutaka Uchiyama, Filip Krajinovic, Pierre-Hugues Herbert and Nikoloz Basilashvili were also first-round winners.
