After a brief stint for Vélez Sársfield, where his form saw him called up for the 1982 FIFA World Cup squad, he moved to Club Atlético River Plate to replace the departing national 'keeper Ubaldo Fillol.

[2] In 1988, he transferred to Spanish club Real Betis where, in 1989, he almost lost a finger during a training session when his wedding ring caught on a nail in the crossbar of the goal.

He was the starting goalkeeper during Argentina's victorious 1986 World Cup campaign, playing in all seven games, conceding just five goals in 630 minutes of football, and keeping three clean sheets.

[8] Goycochea eventually became key to Argentina's run to the final, saving penalty shoot-out kicks in the quarter-final win over Yugoslavia and the semi-final victory over hosts Italy.

After resigning from Olimpia due to a "lack of support from the president",[10] he then became coach of UANL Tigres in Mexico, reaching the final of the 2003–04 Primera División de México championship.