He spent the better part of his 16-year senior career with Atlético Madrid, playing 356 competitive games and scoring seven goals.

[1] A Spain international in the 60s, Rivilla represented the nation in two World Cups and the 1964 European Championship, winning the latter tournament.

[4] Already reconverted to a right back, Rivilla was an undisputed starter for the Colchoneros in the following years, notably winning two Copa del Generalísimo trophies and the 1966 national championship, contributing one goal[5] from 24 appearances to the latter conquest.

[6][1] After having Pelé and Santos FC appear at his testimonial match in September 1969, one year after retiring at 32, Rivilla went on to work in home appliance and act as president of Atlético's veterans association.

[7][1] Rivilla won 26 caps for the Spain national team over five years, his debut coming on 10 July 1960 in a 3–1 away friendly win against Peru.