Third seed Kontaveit, who won this competition last year, retired when a set down to Tereza Martincova, while world number seven Maria Sakkari was defeated 5-7 7-5 7-5 by 21-year-old American Alycia Parks in a big upset.
Parks lost the opener but found two crucial breaks of serve when 6-5 up in both the second and third sets to eliminate the fourth seed.
The withdrawal of Belinda Bencica – seeded sixth – with a foot injury put Barbora Krejcikova into the quarter-finals, while Ekaterina Alexandrova will also be in the last eight after overcoming fifth seed Daria Kasatkina 6-1 7-6 (7-1).
The tournament favourites were in much better form at the Jasmin Open in Tunisia, as the top two seeds sealed their places in the quarter-finals with straight-sets wins.
Favourite Ons Jabeur cruised to a 6-1 6-3 victory over Evgeniya Rodina, converting four of her seven break points to safely advance to the next round of her home tournament.
And number two seed Veronika Kudermetova eased past Magdalena Frech 6-3 6-4 to set up a quarter-final meeting with Diane Parry.
The 26-year-old won five out of the final six games as she stormed to the first set, before securing her place in the quarter-finals with a superb second set in which she broke Martincova four times.
Fellow Estonian Kaia Kanepi is also through to the quarter-finals after a 7-5 7-5 victory over Ann Li.
The world number 32 found a crucial break with the opener tied at 5-5 as she took the first set, before breaking Li three times in the second to seal the win.
Eighth seed Shuai Zhang was dumped out by Donna Vekic in a 6-2 6-4 defeat, while fellow seed Jil Teichmann also saw her tournament ended as Ysaline Bonaventure beat her 7-6 (10-8) 6-3.
At the Parma Ladies Open, top seed Maria Sakkari came from a set down for the second consecutive match to overcome Maryna Zanevska and reach the semi-finals.
Zanevska sparked hopes for an upset as she broke the world number seven three times on her way to taking the opening set.
But Sakkari improved in the second to tie the match, before overcoming two breaks of serve from her Belgian opponent to win six of the last seven games and earn a 2-6 6-4 6-4 success.
Sakkari will face Danka Kovinic in the semi-finals, after the 27-year-old's 6-4 6-4 triumph over Italian Jasmine Paolini.
Irina-Camelia Begu's run of 12 consecutive wins on clay came to an end as she was defeated 6-2 7-6 (8-6) by Ana Bogdan in an all-Romanian clash.
Bogdan's opponent in the final four will be Mayar Sherif, who beat American Lauren Davis 7-6 (7-2) 6-3.
World number 60 Martincova recorded a 7-6 (7-1) 7-5 triumph over France's Oceane Dodin to ease into the second round in Nottingham.
Heather Watson, ranked 102nd in the world, had no problems as she eased past Katie Volynets 6-4 6-2, and fellow Briton Hannah Dart followed suit by defeating Donna Vekic 6-4 6-3.
Jodie Burrage completed the first-round sweep for British women, downing Lin Zhu 7-6 (7-5) 6-4.
At the Rosmalen Grass Court Championship, top seed Aryna Sabalenka was due to face Kateryna Baindl but bad weather curtailed the day's play early.
Earlier on, Anna Kalinskaya edged out Suzan Lamens 7-6 (7-5) 6-3 in the first round, while Catherine McNally, Storm Sanders, Olivia Gadecki and Jamie Loeb were all triumphant in qualifying.
The 18-year-old Czech was impressive against the third seed as she recorded her first win against anyone in the top 30 of the world rankings.
Fourth seed Veronika Kudermetova eased past Amanda Anisimova in just an hour and 15 minutes, winning 6-3 6-0, while Liudmila Samsonova will face second seed Aryna Sabalenka in the next round after coming from a set down to beat Zhang Shuai 5-7 6-3 6-0.
Irina-Camelia Begu and Elena Rybakina also both came from behind to secure wins, with the latter beating fifth seed Danielle Collins to set up a last-16 clash against Ukrainian Marta Kostyuk, who beat Jaimee Fourlis 6-1 3-6 6-4.
At the ASB Classic in Auckland, 42-year-old Venus Williams comfortably overcame her 21-year-old opponent Katie Volynets 7-6 (7-4) 6-2, and will play China's Zhu Lin next after she eliminated sixth seed Madison Brengle 4-6 7-6 (8-6) 6-4.
Third seed Leylah Fernandez beat Brenda Fruhvirtova 6-1 6-1 to set up a last-16 tie with Julia Grabher after she defeated Tereza Martincova in three sets.
Eighth seed Rebecca Marino is through after beating Dalma Galfi in straight sets and will now face Ysaline Bonaventure, who eventually put away Caty McNally 5-7 6-4 6-4.
Viktoria Kuzmova led fourth seed Bernarda Pera 5-4 in the opening set when rain stopped play for the day.
Zhang was never in danger against her unseeded opponent, easing to a 6-2 7-6 (7-4) win to set up a last-eight clash with Tereza Martincova.
Martincova brushed aside number eight seed Magda Linette 6-2 7-6 (7-3) in their round-of-16 meeting on Wednesday.
Elsewhere, Viktorija Golubic beat Heather Watson 7-5 6-2, while the match between number three seed Camila Giorgi and Harriet Dart was suspended at the start of the third set after the Briton had made it one set each.
Meanwhile, rain caused havoc at the Rosmalen Grass Court Championships, with top seed Aryna Sabalenka's match against Arianne Hartono the only one to partially take place.
The match was called off for the day after Sabalenka had claimed the first set 6-2.
