Born in Abanto y Ciérvana-Abanto Zierbena, Biscay, Sarabia came through the ranks of Lezama, Athletic Bilbao's prolific youth system, making his debut for the main squad on 19 September 1976 in a 1–1 home draw against CD Málaga.

He was particularly determined to succeed at the club after his elder brother was rejected due to his birthplace in Torres, Jaén (despite spending most of his life in Biscay), as this did not fit the criteria for their signing policy at the time.

[3] A full first-team member from 1978–79 onwards, having served a loan with neighbours Barakaldo CF the previous year,[3] Sarabia went on to appear in 284 La Liga matches for the Basques with 83 goals.

He had a best output of 16 in the 1982–83 season when Athletic won the league title, renewing it the following campaign); during his spell at the San Mamés Stadium, he was also involved in a spat with manager Javier Clemente.

[10][11][12] Sarabia's son, Eder, was also a footballer, albeit only in the amateur level, before becoming a coach with youth teams such as Danok Bat CF and serving as assistant to Quique Setién (former teammate of his father) at UD Las Palmas.