Cabezas Hurtado is a product of Real Cartagena's academy:[2] he made his professional debut for the club on 14 April 2021, coming on as a substitute in the second half of the Copa Colombia match against Llaneros, which ended in a 0–0 draw.[3] The striker scored his first senior goal on 27 February 2022, netting the winner in a 1–2 Categoría Primera B victory over Real Santander.[4] Then, on 20 April of the same year, he scored his first brace in a 3–1 league win over Boyacá Chicó.[5]
On 3 October 2022, it was officially announced that Cabezas Hurtado had agreed to join EFL Championship side Watford on a permanent deal, signing a contract that would begin in the summer of 2023 and last until 2029.[6][7][8] However, on 19 December of the same year, the transfer's activation was anticipated to January 2023, as the forward was officially set to join Categoría Primera A side Independiente Medellín on a six-month loan, with an option to extend the deal until the end of the 2023 season.[9]
On 8 March of the same year, Cabezas Hurtado made his Copa Libertadores debut, coming on for Miguel Monsalve at the 64th minute of a 1–1 draw against Magallanes, in the first leg of the third qualifying stage.[10] Four days later, he also made his league debut, starting in a 2–0 defeat to Boyacá Chicó.[11] Finally, on 15 March, he featured in the second leg of the Copa Libertadores tie against Magallanes, which saw DIM gain a 2–0 win and advance to the group stage of the competition.[12]
On 6 January 2024, Cabezas Hurtado made his Watford debut as a substitute in a 2–1 FA Cup win over Chesterfield, providing the assist for Tom Dele-Bashiru's injury time winner.[16]
On 1 February 2024, Cabezas Hurtado joined EFL League Two side Gillingham on loan for the remainder of the 2023–24 season.[17] He made his league debut for the Kent-based side two days later, coming on as a substitute in the 63rd minute of a 1–1 home draw with Walsall.[18] In his third appearance for the club, he sustained a knee injury, which ultimately forced him to return to his parent club for treatment.[19]
On 15 August 2024, Cabezas Hurtado joined Greek side PAOK on a season-long loan, with an option to buy.[20]
In May 2022, he was included in the Colombian squad that took part in the Maurice Revello Tournament in France,[21] where he scored a goal in the last group stage match against Japan,[7][23][24] as the Cafeteros eventually finished in fourth place.[25][26]
Hurtado's manager at Watford Valérien Ismaël has described him as a "a left-footed and strong No.9, fast and with great intensity to press" and "very clinical in front of goal".[15]Stephen Clemence, who managed him during his Gillingham loan, noted his ability to "do things that other players can’t do at times, that South American movement, snake hips".[19]