Nicknamed Piru, Gaínza's entire career was spent with Athletic Bilbao. Born in Basauri, Biscay, he made his La Liga debut on 13 October 1940 in a 0–1 away loss against Hércules CF, then proceeded to play a total of 19 seasons in the competition with the club, amassing totals of 381 games and 120 goals.
During his spell with the Lions Gaínza won ten major titles, including two national championships and seven Copa del Generalísimo trophies, appearing in a record nine finals in the latter tournament. He retired at the end of the 1958–59 campaign at the age of 37, having appeared in nearly 500 official matches.
Gaínza coached Athletic during four seasons in the 60s. He was sacked just six games into 1968–69, being replaced by former club teammate Rafael Iriondo who led the side to the domestic cup conquest. He died on 6 January 1995 in his hometown, at 72.