In 2007, she won tournaments in Antalya and Bucharest and made her first WTA Tour main draw appearances, the highlight of which was a semifinal in Stockholm, where she lost to Vera Dushevina in three sets.

Görges made her Grand Slam main draw debut at the US Open, losing to Justine Henin in the first round in straight sets.

Her best performances were reaching the semifinals of the Slovenia Open, where she lost to Anabel Medina Garrigues, and a quarterfinal-loss to Olga Govortsova in the Cellular South Cup.

[7] At the Gastein Ladies, Görges won her first career WTA singles title by defeating Timea Bacsinszky in the final in straight sets.

At the Danish Open, she reached the quarterfinals, but was unable to take advantage of a 5–3 third-set lead over the top seed Wozniacki, eventually falling in a tiebreak.

At the Family Circle Cup in Charleston, however, she made a quarterfinal appearance on the green clay, losing to Elena Vesnina in three sets.

Seeded fifth at the Auckland Open, she defeated the defending champion Gréta Arn, before falling to her compatriot Angelique Kerber in straight sets.

Görges experienced more success in doubles, reaching the final with Flavia Pennetta before falling to the Czech duo of Andrea Hlaváčková and Lucie Hradecká in a third-set super tiebreak.

Görges defeated Polona Hercog, Eleni Daniilidou, and Romina Oprandi, before being dominated by the eighth seed Agnieszka Radwańska.

She defeated Svetlana Kuznetsova, Casey Dellacqua and Daniela Hantuchová, scored a two-set win over the third seed Caroline Wozniacki, but then fell to Agnieszka Radwańska again.

Seeded eighteenth at the Australian Open, Görges advanced to the fourth round after wins over Vera Dushevina, Romina Oprandi, and Zheng Jie.

[25] Seeded fourth at the first edition of the Katowice Open, Görges retired during her first-round match against qualifier Jill Craybas due to dizziness.

[28] In the Madrid Open, Görges defeated Bojana Jovanovski in round one but withdrew from her second-round match against Varvara Lepchenko because of an infection.

In Brussels she reached the second round, after defeating CoCo Vandeweghe, but retired the match against Romina Oprandi due to a right wrist injury.

This result was followed by a series of first-round losses: against Mariana Duque at Wimbledon, against Olga Govortsova in Stanford, against Sesil Karatantcheva in Carlsbad, against Roberta Vinci in Toronto and against Magdaléna Rybáriková in Cincinnati.

Alongside Darija Jurak, she reached the final in Stanford, where they lost to the American pair Raquel Kops-Jones and Abigail Spears.

In New Haven, Görges won her first-round match against Bojana Jovanovski, but lost in the second round to the sixth seed Sloane Stephens.

She lost her openers in her final three tournaments of 2013; against Sorana Cîrstea in Tokyo, against Kaia Kanepi in Beijing and against the qualifier Camila Giorgi in Linz.

In Sydney, Görges retired in the final round of qualifying but was awarded a lucky loser spot in the main draw, where she lost to Caroline Wozniacki.

[34] The following week, Görges competed in Acapulco where she defeated the Mexican wildcard Marcela Zacarías in the first round before losing to Kaia Kanepi in three sets.

In doubles, Görges was the top seed alongside Katarzyna Piter, but they could only make the quarterfinals, losing to the British pairing of Jocelyn Rae and Anna Smith.

Görges won a dead rubber playing in the doubles alongside Sabine Lisicki in the Fed Cup match against Australia.

[38] At the Australian Open, she defeated Andreea Mitu before losing in straight sets to her doubles partner, the ninth seed Karolína Plíšková.

In the doubles, Görges and Karolína Plíšková reached the semifinals, where they lost to the top seeds and eventual winners, Hingis and Mirza.

[55] In April, she reached final of Premier tournament in Charleston, defeating Naomi Osaka, Daria Kasatkina and Anastasija Sevastova.

At Wimbledon, Görges reached her first Grand Slam semifinal, defeating Monica Puig, Vera Lapko, Barbora Strýcová, Donna Vekić and Kiki Bertens en route.

[65] At Wimbledon, Görges defeated Elena-Gabriela Ruse and Varvara Flink before losing in the third round to Serena Williams, in a rematch of the previous year's semifinal.

[66] At the US Open, Görges defeated Natalia Vikhlyantseva, Francesca Di Lorenzo, and Kiki Bertens to reach the fourth round, where she lost to Donna Vekić, despite having a match point in the second set.

[67] Görges attempted to defend her title at Luxembourg, and reached the final after defeating Misaki Doi, Sorana Cîrstea, Monica Puig, and Elena Rybakina.

She partnered Caroline Garcia in doubles, and reached the quarterfinals, where they fell to eventual champions Asia Muhammad and Taylor Townsend.