She first came to prominence by reaching the quarterfinals of the 2008 French Open as a qualifier, in what was her first appearance in the main draw of a Grand Slam tournament.

Suárez Navarro reached the second Grand Slam quarterfinal of her career at the 2009 Australian Open before being defeated by Elena Dementieva, 6–2, 6–2.

In March, Suárez Navarro reached her first final on the WTA Tour at the Andalucia Tennis Experience, a clay court event in Marbella, Spain.

At Roland Garros seeded 22, she defeated Edina Gallovits 6–1, 6–4 and Lucie Hradecká 6–2, 6–4, before losing to Victoria Azarenka in the third round.

She faced defending champion Venus Williams for the first time since the 2009 Australian Open but was unable to repeat the upset win, losing 0–6, 4–6.

Suárez Navarro had a good start to 2010, making the second round of the Auckland Open before losing to top seed Flavia Pennetta, in straight sets.

At the Australian Open, Suárez Navarro made it to the third round before losing to top seed, the defending (and eventual) champion Serena Williams, 0–6, 3–6.

Unseeded at the Indian Wells Open, Suárez Navarro reached the fourth round, losing to Alisa Kleybanova 6–2, 6–7, 4–6.

She reached the final of the Andalucia Tennis Experience in Marbella for the second year in a row, losing to Flavia Pennetta 2–6, 6–4, 3–6.

Going into the Australian Open, she defeated American Christina McHale but lost to eventual titlist Kim Clijsters of Belgium in the following round.

Next, she represented Spain at the Fed Cup against Estonia in Tallinn, where she had a 1–1 record, getting past Anett Kontaveit but falling to Kaia Kanepi.

She returned to the competition at the Open de Marseille, where she beat Sun Shengnan and Aleksandra Wozniak to make the quarterfinals, but was beaten by home crowd favourite Pauline Parmentier.

In early September, Suárez reached round four of the US Open for the first time, defeating Mathilde Johansson, Simona Halep and compatriot Sílvia Soler Espinosa.

[4] At the London Olympics, she beat Samantha Stosur in a thrilling first-round match, 3–6, 7–5, 10–8,[5] avenging her first round defeat to the Australian at Wimbledon the previous month.

At the Dubai Tennis Championships, she received a first round bye but fell to eventual semifinalist Caroline Garcia.

Her next tournament was the Qatar Open where she also received a first-round bye and defeated Donna Vekić, Timea Bacsinszky, Elena Vesnina and Agnieszka Radwańska en route to the final, ensuring a new career-high ranking of world No.

[6] In April 2021, Suárez Navarro announced that her cancer was in complete remission, and that she would commence a farewell tour beginning at Roland-Garros and culminating in a final US Open appearance.