[4][5] In a first-round contest between two qualifiers, Carballés Baena recorded his first ATP World Tour win at the 2014 Casablanca Open when he defeated David Goffin of Belgium in straight sets.

In March 2016, Carballés Baena made his Masters 1000 debut as a wildcard at the Miami Open, losing to Aljaž Bedene in three sets in the first round.

The following month, he made his debut at his home Masters, the Mutua Madrid Open, where he won two qualifying matches to reach the main draw.

In February 2018, Carballés Baena won his first ATP title at the Ecuador Open Quito, defeating second seed Albert Ramos Viñolas in the final.

Carballés Baena qualified to represent Spain at the 2020 Summer Olympics in singles and doubles partnering with Pablo Andujar.

At the Firenze Open, Carballés Baena advanced to his 15th ATP quarterfinal, his first on a surface other than clay, defeating second seed Matteo Berrettini, his third victory over a top-20 player.

[8] At the Córdoba Open in February, Carballés Baena broke the record for the longest match ever in tournament history when he lost to compatriot Bernabe Zapata Miralles in three hours and 26 minutes in the first round.

[12] At the French Open, Carballés Baena defeated qualifier Emilio Nava before losing to fifth seed Stefanos Tsitsipas in the second round.

After losing to Tallon Griekspoor in the first round of the Halle Open, Carballés Baena competed at the Mallorca Championships as the eighth seed, defeating Ilya Ivashka in three sets to record his fifth career win on grass.